diff --git a/doc/source/whatsnew/v1.0.0.rst b/doc/source/whatsnew/v1.0.0.rst
index 4671170fa79ae..c6c5562af3951 100644
--- a/doc/source/whatsnew/v1.0.0.rst
+++ b/doc/source/whatsnew/v1.0.0.rst
@@ -716,7 +716,7 @@ Datetimelike
 - Bug in :class:`DatetimeIndex` addition when adding a non-optimized :class:`DateOffset` incorrectly dropping timezone information (:issue:`30336`)
 - Bug in :meth:`DataFrame.drop` where attempting to drop non-existent values from a DatetimeIndex would yield a confusing error message (:issue:`30399`)
 - Bug in :meth:`DataFrame.append` would remove the timezone-awareness of new data (:issue:`30238`)
-
+- Bug in :class:`DatetimeArray`, :class:`TimedeltaArray`, and :class:`PeriodArray` where inplace addition and subtraction did not actually operate inplace (:issue:`24115`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index ff21a66928294..66f0ad2500c54 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1311,14 +1311,23 @@ def __rsub__(self, other):
 
         return -(self - other)
 
-    # FIXME: DTA/TDA/PA inplace methods should actually be inplace, GH#24115
     def __iadd__(self, other):  # type: ignore
-        # alias for __add__
-        return self.__add__(other)
+        result = self + other
+        self[:] = result[:]
+
+        if not is_period_dtype(self):
+            # restore freq, which is invalidated by setitem
+            self._freq = result._freq
+        return self
 
     def __isub__(self, other):  # type: ignore
-        # alias for __sub__
-        return self.__sub__(other)
+        result = self - other
+        self[:] = result[:]
+
+        if not is_period_dtype(self):
+            # restore freq, which is invalidated by setitem
+            self._freq = result._freq
+        return self
 
     # --------------------------------------------------------------
     # Comparison Methods
diff --git a/pandas/tests/arrays/test_datetimelike.py b/pandas/tests/arrays/test_datetimelike.py
index 84b6d45b78fe8..e9c64d04ec860 100644
--- a/pandas/tests/arrays/test_datetimelike.py
+++ b/pandas/tests/arrays/test_datetimelike.py
@@ -225,6 +225,19 @@ def test_setitem_raises(self):
         with pytest.raises(TypeError, match="'value' should be a.* 'object'"):
             arr[0] = object()
 
+    def test_inplace_arithmetic(self):
+        # GH#24115 check that iadd and isub are actually in-place
+        data = np.arange(10, dtype="i8") * 24 * 3600 * 10 ** 9
+        arr = self.array_cls(data, freq="D")
+
+        expected = arr + pd.Timedelta(days=1)
+        arr += pd.Timedelta(days=1)
+        tm.assert_equal(arr, expected)
+
+        expected = arr - pd.Timedelta(days=1)
+        arr -= pd.Timedelta(days=1)
+        tm.assert_equal(arr, expected)
+
 
 class TestDatetimeArray(SharedTests):
     index_cls = pd.DatetimeIndex