diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index f8cb99e2b2e75..06b6d4242e622 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -8522,6 +8522,12 @@ def idxmin(self, axis=0, skipna=True) -> Series:
         """
         axis = self._get_axis_number(axis)
         indices = nanops.nanargmin(self.values, axis=axis, skipna=skipna)
+
+        # indices will always be np.ndarray since axis is not None and
+        # values is a 2d array for DataFrame
+        # error: Item "int" of "Union[int, Any]" has no attribute "__iter__"
+        assert isinstance(indices, np.ndarray)  # for mypy
+
         index = self._get_axis(axis)
         result = [index[i] if i >= 0 else np.nan for i in indices]
         return Series(result, index=self._get_agg_axis(axis))
@@ -8589,6 +8595,12 @@ def idxmax(self, axis=0, skipna=True) -> Series:
         """
         axis = self._get_axis_number(axis)
         indices = nanops.nanargmax(self.values, axis=axis, skipna=skipna)
+
+        # indices will always be np.ndarray since axis is not None and
+        # values is a 2d array for DataFrame
+        # error: Item "int" of "Union[int, Any]" has no attribute "__iter__"
+        assert isinstance(indices, np.ndarray)  # for mypy
+
         index = self._get_axis(axis)
         result = [index[i] if i >= 0 else np.nan for i in indices]
         return Series(result, index=self._get_agg_axis(axis))
diff --git a/pandas/core/nanops.py b/pandas/core/nanops.py
index 32b05872ded3f..d74a6ba605666 100644
--- a/pandas/core/nanops.py
+++ b/pandas/core/nanops.py
@@ -1,14 +1,14 @@
 import functools
 import itertools
 import operator
-from typing import Any, Optional, Tuple, Union
+from typing import Any, Optional, Tuple, Union, cast
 
 import numpy as np
 
 from pandas._config import get_option
 
 from pandas._libs import NaT, Timedelta, Timestamp, iNaT, lib
-from pandas._typing import ArrayLike, Dtype, Scalar
+from pandas._typing import ArrayLike, Dtype, F, Scalar
 from pandas.compat._optional import import_optional_dependency
 
 from pandas.core.dtypes.cast import _int64_max, maybe_upcast_putmask
@@ -57,7 +57,7 @@ def __init__(self, *dtypes):
     def check(self, obj) -> bool:
         return hasattr(obj, "dtype") and issubclass(obj.dtype.type, self.dtypes)
 
-    def __call__(self, f):
+    def __call__(self, f: F) -> F:
         @functools.wraps(f)
         def _f(*args, **kwargs):
             obj_iter = itertools.chain(args, kwargs.values())
@@ -78,7 +78,7 @@ def _f(*args, **kwargs):
                     raise TypeError(e) from e
                 raise
 
-        return _f
+        return cast(F, _f)
 
 
 class bottleneck_switch:
@@ -878,7 +878,7 @@ def nanargmax(
     axis: Optional[int] = None,
     skipna: bool = True,
     mask: Optional[np.ndarray] = None,
-) -> int:
+) -> Union[int, np.ndarray]:
     """
     Parameters
     ----------
@@ -890,15 +890,25 @@ def nanargmax(
 
     Returns
     -------
-    result : int
-        The index of max value in specified axis or -1 in the NA case
+    result : int or ndarray[int]
+        The index/indices  of max value in specified axis or -1 in the NA case
 
     Examples
     --------
     >>> import pandas.core.nanops as nanops
-    >>> s = pd.Series([1, 2, 3, np.nan, 4])
-    >>> nanops.nanargmax(s)
+    >>> arr = np.array([1, 2, 3, np.nan, 4])
+    >>> nanops.nanargmax(arr)
     4
+
+    >>> arr = np.array(range(12), dtype=np.float64).reshape(4, 3)
+    >>> arr[2:, 2] = np.nan
+    >>> arr
+    array([[ 0.,  1.,  2.],
+           [ 3.,  4.,  5.],
+           [ 6.,  7., nan],
+           [ 9., 10., nan]])
+    >>> nanops.nanargmax(arr, axis=1)
+    array([2, 2, 1, 1], dtype=int64)
     """
     values, mask, dtype, _, _ = _get_values(
         values, True, fill_value_typ="-inf", mask=mask
@@ -914,7 +924,7 @@ def nanargmin(
     axis: Optional[int] = None,
     skipna: bool = True,
     mask: Optional[np.ndarray] = None,
-) -> int:
+) -> Union[int, np.ndarray]:
     """
     Parameters
     ----------
@@ -926,15 +936,25 @@ def nanargmin(
 
     Returns
     -------
-    result : int
-        The index of min value in specified axis or -1 in the NA case
+    result : int or ndarray[int]
+        The index/indices of min value in specified axis or -1 in the NA case
 
     Examples
     --------
     >>> import pandas.core.nanops as nanops
-    >>> s = pd.Series([1, 2, 3, np.nan, 4])
-    >>> nanops.nanargmin(s)
+    >>> arr = np.array([1, 2, 3, np.nan, 4])
+    >>> nanops.nanargmin(arr)
     0
+
+    >>> arr = np.array(range(12), dtype=np.float64).reshape(4, 3)
+    >>> arr[2:, 0] = np.nan
+    >>> arr
+    array([[ 0.,  1.,  2.],
+           [ 3.,  4.,  5.],
+           [nan,  7.,  8.],
+           [nan, 10., 11.]])
+    >>> nanops.nanargmin(arr, axis=1)
+    array([0, 0, 1, 1], dtype=int64)
     """
     values, mask, dtype, _, _ = _get_values(
         values, True, fill_value_typ="+inf", mask=mask