diff --git a/pandas/core/series.py b/pandas/core/series.py
index f0f5bd7c3e2b2..a53d65edabec2 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -4604,8 +4604,17 @@ def set_axis(self, labels, axis: Axis = 0, inplace: bool = False):
         optional_labels=_shared_doc_kwargs["optional_labels"],
         optional_axis=_shared_doc_kwargs["optional_axis"],
     )
-    def reindex(self, index=None, **kwargs):
-        return super().reindex(index=index, **kwargs)
+    def reindex(self, *args, **kwargs) -> Series:
+        if len(args) > 1:
+            raise TypeError("Only one positional argument ('index') is allowed")
+        if args:
+            (index,) = args
+            if "index" in kwargs:
+                raise TypeError(
+                    "'index' passed as both positional and keyword argument"
+                )
+            kwargs.update({"index": index})
+        return super().reindex(**kwargs)
 
     @deprecate_nonkeyword_arguments(version=None, allowed_args=["self", "labels"])
     def drop(
diff --git a/pandas/tests/series/methods/test_reindex.py b/pandas/tests/series/methods/test_reindex.py
index be9f96c8b509a..4350a5d9ac989 100644
--- a/pandas/tests/series/methods/test_reindex.py
+++ b/pandas/tests/series/methods/test_reindex.py
@@ -348,6 +348,31 @@ def test_reindex_periodindex_with_object(p_values, o_values, values, expected_va
     tm.assert_series_equal(result, expected)
 
 
+def test_reindex_too_many_args():
+    # GH 40980
+    ser = Series([1, 2])
+    with pytest.raises(
+        TypeError, match=r"Only one positional argument \('index'\) is allowed"
+    ):
+        ser.reindex([2, 3], False)
+
+
+def test_reindex_double_index():
+    # GH 40980
+    ser = Series([1, 2])
+    msg = r"'index' passed as both positional and keyword argument"
+    with pytest.raises(TypeError, match=msg):
+        ser.reindex([2, 3], index=[3, 4])
+
+
+def test_reindex_no_posargs():
+    # GH 40980
+    ser = Series([1, 2])
+    result = ser.reindex(index=[1, 0])
+    expected = Series([2, 1], index=[1, 0])
+    tm.assert_series_equal(result, expected)
+
+
 @pytest.mark.parametrize("values", [[["a"], ["x"]], [[], []]])
 def test_reindex_empty_with_level(values):
     # GH41170