diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 23c61773daf5a..260ff67742e97 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -4541,6 +4541,26 @@ def align(
             broadcast_axis=broadcast_axis,
         )
 
+    @overload
+    def set_axis(
+        self, labels, axis: Axis = ..., inplace: Literal[False] = ...
+    ) -> DataFrame:
+        ...
+
+    @overload
+    def set_axis(self, labels, axis: Axis, inplace: Literal[True]) -> None:
+        ...
+
+    @overload
+    def set_axis(self, labels, *, inplace: Literal[True]) -> None:
+        ...
+
+    @overload
+    def set_axis(
+        self, labels, axis: Axis = ..., inplace: bool = ...
+    ) -> Optional[DataFrame]:
+        ...
+
     @Appender(
         """
         Examples
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 050550f8add50..0b89cd83e4f76 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -24,6 +24,7 @@
     Type,
     Union,
     cast,
+    overload,
 )
 import warnings
 import weakref
@@ -162,6 +163,8 @@
 from pandas.io.formats.printing import pprint_thing
 
 if TYPE_CHECKING:
+    from typing import Literal
+
     from pandas._libs.tslibs import BaseOffset
 
     from pandas.core.frame import DataFrame
@@ -682,6 +685,28 @@ def _obj_with_exclusions(self: FrameOrSeries) -> FrameOrSeries:
         """ internal compat with SelectionMixin """
         return self
 
+    @overload
+    def set_axis(
+        self: FrameOrSeries, labels, axis: Axis = ..., inplace: Literal[False] = ...
+    ) -> FrameOrSeries:
+        ...
+
+    @overload
+    def set_axis(
+        self: FrameOrSeries, labels, axis: Axis, inplace: Literal[True]
+    ) -> None:
+        ...
+
+    @overload
+    def set_axis(self: FrameOrSeries, labels, *, inplace: Literal[True]) -> None:
+        ...
+
+    @overload
+    def set_axis(
+        self: FrameOrSeries, labels, axis: Axis = ..., inplace: bool = ...
+    ) -> Optional[FrameOrSeries]:
+        ...
+
     def set_axis(self, labels, axis: Axis = 0, inplace: bool = False):
         """
         Assign desired index to given axis.
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 1f5a42265ec98..662c7abb33e33 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -20,6 +20,7 @@
     Type,
     Union,
     cast,
+    overload,
 )
 import warnings
 
@@ -142,6 +143,8 @@
 import pandas.plotting
 
 if TYPE_CHECKING:
+    from typing import Literal
+
     from pandas._typing import (
         TimedeltaConvertibleTypes,
         TimestampConvertibleTypes,
@@ -4342,6 +4345,26 @@ def rename(
         else:
             return self._set_name(index, inplace=inplace)
 
+    @overload
+    def set_axis(
+        self, labels, axis: Axis = ..., inplace: Literal[False] = ...
+    ) -> Series:
+        ...
+
+    @overload
+    def set_axis(self, labels, axis: Axis, inplace: Literal[True]) -> None:
+        ...
+
+    @overload
+    def set_axis(self, labels, *, inplace: Literal[True]) -> None:
+        ...
+
+    @overload
+    def set_axis(
+        self, labels, axis: Axis = ..., inplace: bool = ...
+    ) -> Optional[Series]:
+        ...
+
     @Appender(
         """
         Examples