diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 8e72ce83ac028..9405e7804a461 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -254,6 +254,7 @@ Groupby/Resample/Rolling
 - Bug in :func:`pandas.core.groupby.GroupBy.agg` when applying a aggregation function to timezone aware data (:issue:`23683`)
 - Bug in :func:`pandas.core.groupby.GroupBy.first` and :func:`pandas.core.groupby.GroupBy.last` where timezone information would be dropped (:issue:`21603`)
 - Ensured that ordering of outputs in ``groupby`` aggregation functions is consistent across all versions of Python (:issue:`25692`)
+- Bug in :func:`idxmax` and :func:`idxmin` on :meth:`DataFrame.groupby` with datetime column would return incorrect dtype (:issue:`25444`, :issue:`15306`)
 
 
 Reshaping
diff --git a/pandas/core/groupby/base.py b/pandas/core/groupby/base.py
index 903c898b68873..a5804586bdf11 100644
--- a/pandas/core/groupby/base.py
+++ b/pandas/core/groupby/base.py
@@ -89,7 +89,8 @@ def _gotitem(self, key, ndim, subset=None):
 cython_transforms = frozenset(['cumprod', 'cumsum', 'shift',
                                'cummin', 'cummax'])
 
-cython_cast_blacklist = frozenset(['rank', 'count', 'size'])
+cython_cast_blacklist = frozenset(['rank', 'count', 'size', 'idxmin',
+                                   'idxmax'])
 
 
 def whitelist_method_generator(base, klass, whitelist):
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index bdae6f36b5572..5823c39cbd8ed 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -254,8 +254,13 @@ def _aggregate_item_by_item(self, func, *args, **kwargs):
                 data = obj[item]
                 colg = SeriesGroupBy(data, selection=item,
                                      grouper=self.grouper)
-                result[item] = self._try_cast(
-                    colg.aggregate(func, *args, **kwargs), data)
+
+                cast = self._transform_should_cast(func)
+
+                result[item] = colg.aggregate(func, *args, **kwargs)
+                if cast:
+                    result[item] = self._try_cast(result[item], data)
+
             except ValueError:
                 cannot_agg.append(item)
                 continue
diff --git a/pandas/tests/groupby/test_function.py b/pandas/tests/groupby/test_function.py
index b5e328ef64424..4ea0d12656ee4 100644
--- a/pandas/tests/groupby/test_function.py
+++ b/pandas/tests/groupby/test_function.py
@@ -400,6 +400,25 @@ def test_groupby_non_arithmetic_agg_int_like_precision(i):
         assert res.iloc[0].b == data["expected"]
 
 
+@pytest.mark.parametrize("func, values", [
+    ("idxmin", {'c_int': [0, 2], 'c_float': [1, 3], 'c_date': [1, 2]}),
+    ("idxmax", {'c_int': [1, 3], 'c_float': [0, 2], 'c_date': [0, 3]})
+])
+def test_idxmin_idxmax_returns_int_types(func, values):
+    # GH 25444
+    df = pd.DataFrame({'name': ['A', 'A', 'B', 'B'],
+                       'c_int': [1, 2, 3, 4],
+                       'c_float': [4.02, 3.03, 2.04, 1.05],
+                       'c_date': ['2019', '2018', '2016', '2017']})
+    df['c_date'] = pd.to_datetime(df['c_date'])
+
+    result = getattr(df.groupby('name'), func)()
+
+    expected = pd.DataFrame(values, index=Index(['A', 'B'], name="name"))
+
+    tm.assert_frame_equal(result, expected)
+
+
 def test_fill_consistency():
 
     # GH9221
diff --git a/pandas/tests/groupby/test_transform.py b/pandas/tests/groupby/test_transform.py
index b645073fcf72a..26f39f8f41e2f 100644
--- a/pandas/tests/groupby/test_transform.py
+++ b/pandas/tests/groupby/test_transform.py
@@ -845,3 +845,22 @@ def test_groupby_transform_timezone_column(func):
     expected = pd.DataFrame([[ts, 1, ts]], columns=['end_time', 'id',
                                                     'max_end_time'])
     tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize("func, values", [
+    ("idxmin", ["1/1/2011"] * 2 + ["1/3/2011"] * 7 + ["1/10/2011"]),
+    ("idxmax", ["1/2/2011"] * 2 + ["1/9/2011"] * 7 + ["1/10/2011"])
+])
+def test_groupby_transform_with_datetimes(func, values):
+    # GH 15306
+    dates = pd.date_range('1/1/2011', periods=10, freq='D')
+
+    stocks = pd.DataFrame({'price': np.arange(10.0)}, index=dates)
+    stocks['week_id'] = pd.to_datetime(stocks.index).week
+
+    result = stocks.groupby(stocks['week_id'])['price'].transform(func)
+
+    expected = pd.Series(data=pd.to_datetime(values),
+                         index=dates, name="price")
+
+    tm.assert_series_equal(result, expected)