diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 4ac737bb6b29a..74a50f435de5d 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -156,6 +156,7 @@ Removal of prior version deprecations/changes
 - Remove arguments ``names`` and ``dtype`` from :meth:`Index.copy` and ``levels`` and ``codes`` from :meth:`MultiIndex.copy` (:issue:`35853`, :issue:`36685`)
 - Remove argument ``inplace`` from :meth:`MultiIndex.set_levels` and :meth:`MultiIndex.set_codes` (:issue:`35626`)
 - Disallow passing positional arguments to :meth:`MultiIndex.set_levels` and :meth:`MultiIndex.set_codes` (:issue:`41485`)
+- Removed argument ``how`` from :meth:`PeriodIndex.astype`, use :meth:`PeriodIndex.to_timestamp` instead (:issue:`37982`)
 - Removed argument ``try_cast`` from :meth:`DataFrame.mask`, :meth:`DataFrame.where`, :meth:`Series.mask` and :meth:`Series.where` (:issue:`38836`)
 - Disallow passing non-round floats to :class:`Timestamp` with ``unit="M"`` or ``unit="Y"`` (:issue:`47266`)
 - Removed deprecated :meth:`Timedelta.delta`, :meth:`Timedelta.is_populated`, and :attr:`Timedelta.freq` (:issue:`46430`, :issue:`46476`)
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index a5408f19456dd..889d8f33cdfae 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -5,7 +5,6 @@
     timedelta,
 )
 from typing import Hashable
-import warnings
 
 import numpy as np
 
@@ -29,13 +28,8 @@
     cache_readonly,
     doc,
 )
-from pandas.util._exceptions import find_stack_level
 
-from pandas.core.dtypes.common import (
-    is_datetime64_any_dtype,
-    is_integer,
-    pandas_dtype,
-)
+from pandas.core.dtypes.common import is_integer
 from pandas.core.dtypes.dtypes import PeriodDtype
 from pandas.core.dtypes.missing import is_valid_na_for_dtype
 
@@ -349,32 +343,6 @@ def asof_locs(self, where: Index, mask: npt.NDArray[np.bool_]) -> np.ndarray:
 
         return super().asof_locs(where, mask)
 
-    @doc(Index.astype)
-    def astype(self, dtype, copy: bool = True, how=lib.no_default):
-        dtype = pandas_dtype(dtype)
-
-        if how is not lib.no_default:
-            # GH#37982
-            warnings.warn(
-                "The 'how' keyword in PeriodIndex.astype is deprecated and "
-                "will be removed in a future version. "
-                "Use index.to_timestamp(how=how) instead.",
-                FutureWarning,
-                stacklevel=find_stack_level(),
-            )
-        else:
-            how = "start"
-
-        if is_datetime64_any_dtype(dtype):
-            # 'how' is index-specific, isn't part of the EA interface.
-            # GH#45038 implement this for PeriodArray (but without "how")
-            #  once the "how" deprecation is enforced we can just dispatch
-            #  directly to PeriodArray.
-            tz = getattr(dtype, "tz", None)
-            return self.to_timestamp(how=how).tz_localize(tz)
-
-        return super().astype(dtype, copy=copy)
-
     @property
     def is_full(self) -> bool:
         """
diff --git a/pandas/tests/indexes/period/methods/test_astype.py b/pandas/tests/indexes/period/methods/test_astype.py
index fbc1d3702115e..9720b751b87ce 100644
--- a/pandas/tests/indexes/period/methods/test_astype.py
+++ b/pandas/tests/indexes/period/methods/test_astype.py
@@ -8,7 +8,6 @@
     NaT,
     Period,
     PeriodIndex,
-    Timedelta,
     period_range,
 )
 import pandas._testing as tm
@@ -149,30 +148,7 @@ def test_astype_array_fallback(self):
     def test_period_astype_to_timestamp(self):
         pi = PeriodIndex(["2011-01", "2011-02", "2011-03"], freq="M")
 
-        exp = DatetimeIndex(["2011-01-01", "2011-02-01", "2011-03-01"], freq="MS")
-        with tm.assert_produces_warning(FutureWarning):
-            # how keyword deprecated GH#37982
-            res = pi.astype("datetime64[ns]", how="start")
-        tm.assert_index_equal(res, exp)
-        assert res.freq == exp.freq
-
-        exp = DatetimeIndex(["2011-01-31", "2011-02-28", "2011-03-31"])
-        exp = exp + Timedelta(1, "D") - Timedelta(1, "ns")
-        with tm.assert_produces_warning(FutureWarning):
-            # how keyword deprecated GH#37982
-            res = pi.astype("datetime64[ns]", how="end")
-        tm.assert_index_equal(res, exp)
-        assert res.freq == exp.freq
-
         exp = DatetimeIndex(["2011-01-01", "2011-02-01", "2011-03-01"], tz="US/Eastern")
         res = pi.astype("datetime64[ns, US/Eastern]")
         tm.assert_index_equal(res, exp)
         assert res.freq == exp.freq
-
-        exp = DatetimeIndex(["2011-01-31", "2011-02-28", "2011-03-31"], tz="US/Eastern")
-        exp = exp + Timedelta(1, "D") - Timedelta(1, "ns")
-        with tm.assert_produces_warning(FutureWarning):
-            # how keyword deprecated GH#37982
-            res = pi.astype("datetime64[ns, US/Eastern]", how="end")
-        tm.assert_index_equal(res, exp)
-        assert res.freq == exp.freq