diff --git a/doc/source/styled.xlsx b/doc/source/styled.xlsx
new file mode 100644
index 0000000000000..1233ff2b8692b
Binary files /dev/null and b/doc/source/styled.xlsx differ
diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index c0e00c7bf6f54..83ca93bdfa703 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -22,6 +22,7 @@ Other Enhancements
 - Indexing of ``DataFrame`` and ``Series`` now accepts zerodim ``np.ndarray`` (:issue:`24919`)
 - :meth:`Timestamp.replace` now supports the ``fold`` argument to disambiguate DST transition times (:issue:`25017`)
 - :meth:`DataFrame.at_time` and :meth:`Series.at_time` now support :meth:`datetime.time` objects with timezones (:issue:`24043`)
+- :meth:`DatetimeIndex.union` now supports the ``sort`` argument. The behaviour of the sort parameter matches that of :meth:`Index.union` (:issue:`24994`)
 -
 
 .. _whatsnew_0250.api_breaking:
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index 1037e2d9a3bd6..a6697e8879b08 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -460,7 +460,7 @@ def _formatter_func(self):
     # --------------------------------------------------------------------
     # Set Operation Methods
 
-    def union(self, other):
+    def union(self, other, sort=None):
         """
         Specialized union for DatetimeIndex objects. If combine
         overlapping ranges with the same DateOffset, will be much
@@ -469,15 +469,29 @@ def union(self, other):
         Parameters
         ----------
         other : DatetimeIndex or array-like
+        sort : bool or None, default None
+            Whether to sort the resulting Index.
+
+            * None : Sort the result, except when
+
+              1. `self` and `other` are equal.
+              2. `self` or `other` has length 0.
+              3. Some values in `self` or `other` cannot be compared.
+                 A RuntimeWarning is issued in this case.
+
+            * False : do not sort the result
+
+            .. versionadded:: 0.25.0
 
         Returns
         -------
         y : Index or DatetimeIndex
         """
+        self._validate_sort_keyword(sort)
         self._assert_can_do_setop(other)
 
         if len(other) == 0 or self.equals(other) or len(self) == 0:
-            return super(DatetimeIndex, self).union(other)
+            return super(DatetimeIndex, self).union(other, sort=sort)
 
         if not isinstance(other, DatetimeIndex):
             try:
@@ -488,9 +502,9 @@ def union(self, other):
         this, other = self._maybe_utc_convert(other)
 
         if this._can_fast_union(other):
-            return this._fast_union(other)
+            return this._fast_union(other, sort=sort)
         else:
-            result = Index.union(this, other)
+            result = Index.union(this, other, sort=sort)
             if isinstance(result, DatetimeIndex):
                 # TODO: we shouldn't be setting attributes like this;
                 #  in all the tests this equality already holds
@@ -563,16 +577,28 @@ def _can_fast_union(self, other):
             # this will raise
             return False
 
-    def _fast_union(self, other):
+    def _fast_union(self, other, sort=None):
         if len(other) == 0:
             return self.view(type(self))
 
         if len(self) == 0:
             return other.view(type(self))
 
-        # to make our life easier, "sort" the two ranges
+        # Both DTIs are monotonic. Check if they are already
+        # in the "correct" order
         if self[0] <= other[0]:
             left, right = self, other
+        # DTIs are not in the "correct" order and we don't want
+        # to sort but want to remove overlaps
+        elif sort is False:
+            left, right = self, other
+            left_start = left[0]
+            loc = right.searchsorted(left_start, side='left')
+            right_chunk = right.values[:loc]
+            dates = _concat._concat_compat((left.values, right_chunk))
+            return self._shallow_copy(dates)
+        # DTIs are not in the "correct" order and we want
+        # to sort
         else:
             left, right = other, self
 
diff --git a/pandas/tests/indexes/datetimes/test_setops.py b/pandas/tests/indexes/datetimes/test_setops.py
index 19009e45ee83a..cf1f75234ec62 100644
--- a/pandas/tests/indexes/datetimes/test_setops.py
+++ b/pandas/tests/indexes/datetimes/test_setops.py
@@ -21,83 +21,107 @@ class TestDatetimeIndexSetOps(object):
           'dateutil/US/Pacific']
 
     # TODO: moved from test_datetimelike; dedup with version below
-    def test_union2(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_union2(self, sort):
         everything = tm.makeDateIndex(10)
         first = everything[:5]
         second = everything[5:]
-        union = first.union(second)
-        assert tm.equalContents(union, everything)
+        union = first.union(second, sort=sort)
+        tm.assert_index_equal(union, everything)
 
         # GH 10149
         cases = [klass(second.values) for klass in [np.array, Series, list]]
         for case in cases:
-            result = first.union(case)
-            assert tm.equalContents(result, everything)
+            result = first.union(case, sort=sort)
+            tm.assert_index_equal(result, everything)
 
     @pytest.mark.parametrize("tz", tz)
-    def test_union(self, tz):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_union(self, tz, sort):
         rng1 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
         other1 = pd.date_range('1/6/2000', freq='D', periods=5, tz=tz)
         expected1 = pd.date_range('1/1/2000', freq='D', periods=10, tz=tz)
+        expected1_notsorted = pd.DatetimeIndex(list(other1) + list(rng1))
 
         rng2 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
         other2 = pd.date_range('1/4/2000', freq='D', periods=5, tz=tz)
         expected2 = pd.date_range('1/1/2000', freq='D', periods=8, tz=tz)
+        expected2_notsorted = pd.DatetimeIndex(list(other2) + list(rng2[:3]))
 
         rng3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
         other3 = pd.DatetimeIndex([], tz=tz)
         expected3 = pd.date_range('1/1/2000', freq='D', periods=5, tz=tz)
+        expected3_notsorted = rng3
 
-        for rng, other, expected in [(rng1, other1, expected1),
-                                     (rng2, other2, expected2),
-                                     (rng3, other3, expected3)]:
+        for rng, other, exp, exp_notsorted in [(rng1, other1, expected1,
+                                                expected1_notsorted),
+                                               (rng2, other2, expected2,
+                                                expected2_notsorted),
+                                               (rng3, other3, expected3,
+                                                expected3_notsorted)]:
 
-            result_union = rng.union(other)
-            tm.assert_index_equal(result_union, expected)
+            result_union = rng.union(other, sort=sort)
+            tm.assert_index_equal(result_union, exp)
 
-    def test_union_coverage(self):
+            result_union = other.union(rng, sort=sort)
+            if sort is None:
+                tm.assert_index_equal(result_union, exp)
+            else:
+                tm.assert_index_equal(result_union, exp_notsorted)
+
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_union_coverage(self, sort):
         idx = DatetimeIndex(['2000-01-03', '2000-01-01', '2000-01-02'])
         ordered = DatetimeIndex(idx.sort_values(), freq='infer')
-        result = ordered.union(idx)
+        result = ordered.union(idx, sort=sort)
         tm.assert_index_equal(result, ordered)
 
-        result = ordered[:0].union(ordered)
+        result = ordered[:0].union(ordered, sort=sort)
         tm.assert_index_equal(result, ordered)
         assert result.freq == ordered.freq
 
-    def test_union_bug_1730(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_union_bug_1730(self, sort):
         rng_a = date_range('1/1/2012', periods=4, freq='3H')
         rng_b = date_range('1/1/2012', periods=4, freq='4H')
 
-        result = rng_a.union(rng_b)
+        result = rng_a.union(rng_b, sort=sort)
         exp = DatetimeIndex(sorted(set(list(rng_a)) | set(list(rng_b))))
         tm.assert_index_equal(result, exp)
 
-    def test_union_bug_1745(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_union_bug_1745(self, sort):
         left = DatetimeIndex(['2012-05-11 15:19:49.695000'])
         right = DatetimeIndex(['2012-05-29 13:04:21.322000',
                                '2012-05-11 15:27:24.873000',
                                '2012-05-11 15:31:05.350000'])
 
-        result = left.union(right)
-        exp = DatetimeIndex(sorted(set(list(left)) | set(list(right))))
+        result = left.union(right, sort=sort)
+        exp = DatetimeIndex(['2012-05-11 15:19:49.695000',
+                             '2012-05-29 13:04:21.322000',
+                             '2012-05-11 15:27:24.873000',
+                             '2012-05-11 15:31:05.350000'])
+        if sort is None:
+            exp = exp.sort_values()
         tm.assert_index_equal(result, exp)
 
-    def test_union_bug_4564(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_union_bug_4564(self, sort):
         from pandas import DateOffset
         left = date_range("2013-01-01", "2013-02-01")
         right = left + DateOffset(minutes=15)
 
-        result = left.union(right)
+        result = left.union(right, sort=sort)
         exp = DatetimeIndex(sorted(set(list(left)) | set(list(right))))
         tm.assert_index_equal(result, exp)
 
-    def test_union_freq_both_none(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_union_freq_both_none(self, sort):
         # GH11086
         expected = bdate_range('20150101', periods=10)
         expected.freq = None
 
-        result = expected.union(expected)
+        result = expected.union(expected, sort=sort)
         tm.assert_index_equal(result, expected)
         assert result.freq is None
 
@@ -112,11 +136,14 @@ def test_union_dataframe_index(self):
         exp = pd.date_range('1/1/1980', '1/1/2012', freq='MS')
         tm.assert_index_equal(df.index, exp)
 
-    def test_union_with_DatetimeIndex(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_union_with_DatetimeIndex(self, sort):
         i1 = Int64Index(np.arange(0, 20, 2))
         i2 = date_range(start='2012-01-03 00:00:00', periods=10, freq='D')
-        i1.union(i2)  # Works
-        i2.union(i1)  # Fails with "AttributeError: can't set attribute"
+        # Works
+        i1.union(i2, sort=sort)
+        # Fails with "AttributeError: can't set attribute"
+        i2.union(i1, sort=sort)
 
     # TODO: moved from test_datetimelike; de-duplicate with version below
     def test_intersection2(self):
@@ -262,11 +289,12 @@ def test_datetimeindex_diff(self, sort):
                           periods=98)
         assert len(dti1.difference(dti2, sort)) == 2
 
-    def test_datetimeindex_union_join_empty(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_datetimeindex_union_join_empty(self, sort):
         dti = date_range(start='1/1/2001', end='2/1/2001', freq='D')
         empty = Index([])
 
-        result = dti.union(empty)
+        result = dti.union(empty, sort=sort)
         assert isinstance(result, DatetimeIndex)
         assert result is result
 
@@ -287,35 +315,40 @@ class TestBusinessDatetimeIndex(object):
     def setup_method(self, method):
         self.rng = bdate_range(START, END)
 
-    def test_union(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_union(self, sort):
         # overlapping
         left = self.rng[:10]
         right = self.rng[5:10]
 
-        the_union = left.union(right)
+        the_union = left.union(right, sort=sort)
         assert isinstance(the_union, DatetimeIndex)
 
         # non-overlapping, gap in middle
         left = self.rng[:5]
         right = self.rng[10:]
 
-        the_union = left.union(right)
+        the_union = left.union(right, sort=sort)
         assert isinstance(the_union, Index)
 
         # non-overlapping, no gap
         left = self.rng[:5]
         right = self.rng[5:10]
 
-        the_union = left.union(right)
+        the_union = left.union(right, sort=sort)
         assert isinstance(the_union, DatetimeIndex)
 
         # order does not matter
-        tm.assert_index_equal(right.union(left), the_union)
+        if sort is None:
+            tm.assert_index_equal(right.union(left, sort=sort), the_union)
+        else:
+            expected = pd.DatetimeIndex(list(right) + list(left))
+            tm.assert_index_equal(right.union(left, sort=sort), expected)
 
         # overlapping, but different offset
         rng = date_range(START, END, freq=BMonthEnd())
 
-        the_union = self.rng.union(rng)
+        the_union = self.rng.union(rng, sort=sort)
         assert isinstance(the_union, DatetimeIndex)
 
     def test_outer_join(self):
@@ -350,16 +383,21 @@ def test_outer_join(self):
         assert isinstance(the_join, DatetimeIndex)
         assert the_join.freq is None
 
-    def test_union_not_cacheable(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_union_not_cacheable(self, sort):
         rng = date_range('1/1/2000', periods=50, freq=Minute())
         rng1 = rng[10:]
         rng2 = rng[:25]
-        the_union = rng1.union(rng2)
-        tm.assert_index_equal(the_union, rng)
+        the_union = rng1.union(rng2, sort=sort)
+        if sort is None:
+            tm.assert_index_equal(the_union, rng)
+        else:
+            expected = pd.DatetimeIndex(list(rng[10:]) + list(rng[:10]))
+            tm.assert_index_equal(the_union, expected)
 
         rng1 = rng[10:]
         rng2 = rng[15:35]
-        the_union = rng1.union(rng2)
+        the_union = rng1.union(rng2, sort=sort)
         expected = rng[10:]
         tm.assert_index_equal(the_union, expected)
 
@@ -388,7 +426,8 @@ def test_intersection_bug(self):
         result = a.intersection(b)
         tm.assert_index_equal(result, b)
 
-    def test_month_range_union_tz_pytz(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_month_range_union_tz_pytz(self, sort):
         from pytz import timezone
         tz = timezone('US/Eastern')
 
@@ -403,10 +442,11 @@ def test_month_range_union_tz_pytz(self):
         late_dr = date_range(start=late_start, end=late_end, tz=tz,
                              freq=MonthEnd())
 
-        early_dr.union(late_dr)
+        early_dr.union(late_dr, sort=sort)
 
     @td.skip_if_windows_python_3
-    def test_month_range_union_tz_dateutil(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_month_range_union_tz_dateutil(self, sort):
         from pandas._libs.tslibs.timezones import dateutil_gettz
         tz = dateutil_gettz('US/Eastern')
 
@@ -421,7 +461,7 @@ def test_month_range_union_tz_dateutil(self):
         late_dr = date_range(start=late_start, end=late_end, tz=tz,
                              freq=MonthEnd())
 
-        early_dr.union(late_dr)
+        early_dr.union(late_dr, sort=sort)
 
 
 class TestCustomDatetimeIndex(object):
@@ -429,35 +469,37 @@ class TestCustomDatetimeIndex(object):
     def setup_method(self, method):
         self.rng = bdate_range(START, END, freq='C')
 
-    def test_union(self):
+    @pytest.mark.parametrize("sort", [None, False])
+    def test_union(self, sort):
         # overlapping
         left = self.rng[:10]
         right = self.rng[5:10]
 
-        the_union = left.union(right)
+        the_union = left.union(right, sort=sort)
         assert isinstance(the_union, DatetimeIndex)
 
         # non-overlapping, gap in middle
         left = self.rng[:5]
         right = self.rng[10:]
 
-        the_union = left.union(right)
+        the_union = left.union(right, sort)
         assert isinstance(the_union, Index)
 
         # non-overlapping, no gap
         left = self.rng[:5]
         right = self.rng[5:10]
 
-        the_union = left.union(right)
+        the_union = left.union(right, sort=sort)
         assert isinstance(the_union, DatetimeIndex)
 
         # order does not matter
-        tm.assert_index_equal(right.union(left), the_union)
+        if sort is None:
+            tm.assert_index_equal(right.union(left, sort=sort), the_union)
 
         # overlapping, but different offset
         rng = date_range(START, END, freq=BMonthEnd())
 
-        the_union = self.rng.union(rng)
+        the_union = self.rng.union(rng, sort=sort)
         assert isinstance(the_union, DatetimeIndex)
 
     def test_outer_join(self):