diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index f992d6aa09ead..c55ee32528e1b 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -202,7 +202,7 @@ Sparse
 
 ExtensionArray
 ^^^^^^^^^^^^^^
--
+- Bug in construction of nullable integer and floating arrays raising ``TypeError`` when passed boolean data containing ``pd.NA`` (:issue:`42137`)
 -
 
 Styler
diff --git a/pandas/core/arrays/floating.py b/pandas/core/arrays/floating.py
index 1acbcf17dfffd..7556bea38242c 100644
--- a/pandas/core/arrays/floating.py
+++ b/pandas/core/arrays/floating.py
@@ -139,6 +139,7 @@ def coerce_to_array(
             "mixed-integer",
             "integer-na",
             "mixed-integer-float",
+            "boolean",
         ]:
             raise TypeError(f"{values.dtype} cannot be converted to a FloatingDtype")
 
diff --git a/pandas/core/arrays/integer.py b/pandas/core/arrays/integer.py
index c9ba762a271bd..b9026c4f680d1 100644
--- a/pandas/core/arrays/integer.py
+++ b/pandas/core/arrays/integer.py
@@ -194,6 +194,7 @@ def coerce_to_array(
             "mixed-integer",
             "integer-na",
             "mixed-integer-float",
+            "boolean",
         ]:
             raise TypeError(f"{values.dtype} cannot be converted to an IntegerDtype")
 
diff --git a/pandas/tests/arrays/floating/test_construction.py b/pandas/tests/arrays/floating/test_construction.py
index 4ce3dd35b538b..ae1041e9a7109 100644
--- a/pandas/tests/arrays/floating/test_construction.py
+++ b/pandas/tests/arrays/floating/test_construction.py
@@ -146,6 +146,7 @@ def test_to_array_integer():
         ([False, True], [0, 1], Float64Dtype(), Float64Dtype()),
         ([False, True], [0, 1], "Float64", Float64Dtype()),
         ([False, True, np.nan], [0, 1, np.nan], Float64Dtype(), Float64Dtype()),
+        ([False, True, pd.NA], [0, 1, pd.NA], Float64Dtype(), Float64Dtype()),
     ],
 )
 def test_to_array_bool(bool_values, values, target_dtype, expected_dtype):
@@ -155,6 +156,18 @@ def test_to_array_bool(bool_values, values, target_dtype, expected_dtype):
     tm.assert_extension_array_equal(result, expected)
 
 
+@pytest.mark.parametrize(
+    "bool_values,expected",
+    [([False, True, False], [0, 1, 0]), ([False, True, pd.NA], [0, 1, pd.NA])],
+)
+def test_construction_from_boolean_array(bool_values, expected):
+    # GH-42137
+    data = pd.array(bool_values, dtype="boolean")
+    result = pd.array(data, dtype="Float64")
+    expected = pd.array(expected, dtype="Float64")
+    tm.assert_extension_array_equal(result, expected)
+
+
 def test_series_from_float(data):
     # construct from our dtype & string dtype
     dtype = data.dtype
diff --git a/pandas/tests/arrays/integer/test_construction.py b/pandas/tests/arrays/integer/test_construction.py
index b48567d37ecaf..d6b61ed44e913 100644
--- a/pandas/tests/arrays/integer/test_construction.py
+++ b/pandas/tests/arrays/integer/test_construction.py
@@ -187,6 +187,7 @@ def test_to_integer_array_float():
         ([False, True], [0, 1], Int64Dtype(), Int64Dtype()),
         ([False, True], [0, 1], "Int64", Int64Dtype()),
         ([False, True, np.nan], [0, 1, np.nan], Int64Dtype(), Int64Dtype()),
+        ([False, True, pd.NA], [0, 1, pd.NA], Int64Dtype(), Int64Dtype()),
     ],
 )
 def test_to_integer_array_bool(
@@ -198,6 +199,18 @@ def test_to_integer_array_bool(
     tm.assert_extension_array_equal(result, expected)
 
 
+@pytest.mark.parametrize(
+    "bool_values,expected",
+    [([False, True, False], [0, 1, 0]), ([False, True, pd.NA], [0, 1, pd.NA])],
+)
+def test_construction_from_boolean_array(bool_values, expected):
+    # GH-42137
+    data = pd.array(bool_values, dtype="boolean")
+    result = pd.array(data, dtype="Int64")
+    expected = pd.array(expected, dtype="Int64")
+    tm.assert_extension_array_equal(result, expected)
+
+
 @pytest.mark.parametrize(
     "values, to_dtype, result_dtype",
     [