diff --git a/lib/ansible/modules/crypto/openssl_privatekey.py b/lib/ansible/modules/crypto/openssl_privatekey.py
index ed6155b0d66..86953e1ed58 100644
--- a/lib/ansible/modules/crypto/openssl_privatekey.py
+++ b/lib/ansible/modules/crypto/openssl_privatekey.py
@@ -19,9 +19,9 @@ short_description: Generate OpenSSL private keys
 description:
     - This module allows one to (re)generate OpenSSL private keys.
     - One can generate L(RSA,https://en.wikipedia.org/wiki/RSA_(cryptosystem)),
-      L(DSA,https://en.wikipedia.org/wiki/Digital_Signature_Algorithm) or
-      L(ECC,https://en.wikipedia.org/wiki/Elliptic-curve_cryptography)
-      private keys.
+      L(DSA,https://en.wikipedia.org/wiki/Digital_Signature_Algorithm),
+      L(ECC,https://en.wikipedia.org/wiki/Elliptic-curve_cryptography) or
+      L(EdDSA,https://en.wikipedia.org/wiki/EdDSA) private keys.
     - Keys are generated in PEM format.
     - "Please note that the module regenerates private keys if they don't match
       the module's options. In particular, if you provide another passphrase
@@ -52,12 +52,13 @@ options:
     type:
         description:
             - The algorithm used to generate the TLS/SSL private key.
-            - Note that C(ECC) requires the C(cryptography) backend.
-            - Depending on the curve, you need a newer version of the cryptography backend.
+            - Note that C(ECC), C(X25519), C(X448), C(Ed25519) and C(Ed448) require the C(cryptography) backend.
+              C(X25519) needs cryptography 2.5 or newer, while C(X448), C(Ed25519) and C(Ed448) require
+              cryptography 2.6 or newer. For C(ECC), the minimal cryptography version required depends on the
+              I(curve) option.
         type: str
         default: RSA
-        #choices: [ DSA, ECC, RSA, X448, X25519, Ed448, Ed25519 ]
-        choices: [ DSA, ECC, RSA ]
+        choices: [ DSA, ECC, Ed25519, Ed448, RSA, X25519, X448 ]
     curve:
         description:
             - Note that not all curves are supported by all versions of C(cryptography).
@@ -239,8 +240,14 @@ else:
     try:
         import cryptography.hazmat.primitives.asymmetric.x25519
         CRYPTOGRAPHY_HAS_X25519 = True
+        try:
+            cryptography.hazmat.primitives.asymmetric.x25519.X25519PrivateKey.private_bytes
+            CRYPTOGRAPHY_HAS_X25519_FULL = True
+        except AttributeError:
+            CRYPTOGRAPHY_HAS_X25519_FULL = False
     except ImportError:
         CRYPTOGRAPHY_HAS_X25519 = False
+        CRYPTOGRAPHY_HAS_X25519_FULL = False
     try:
         import cryptography.hazmat.primitives.asymmetric.x448
         CRYPTOGRAPHY_HAS_X448 = True
@@ -467,6 +474,8 @@ class PrivateKeyCryptography(PrivateKeyBase):
         self.curve = module.params['curve']
         if not CRYPTOGRAPHY_HAS_X25519 and self.type == 'X25519':
             self.module.fail_json(msg='Your cryptography version does not support X25519')
+        if not CRYPTOGRAPHY_HAS_X25519_FULL and self.type == 'X25519':
+            self.module.fail_json(msg='Your cryptography version does not support X25519 serialization')
         if not CRYPTOGRAPHY_HAS_X448 and self.type == 'X448':
             self.module.fail_json(msg='Your cryptography version does not support X448')
         if not CRYPTOGRAPHY_HAS_ED25519 and self.type == 'Ed25519':
@@ -475,6 +484,7 @@ class PrivateKeyCryptography(PrivateKeyBase):
             self.module.fail_json(msg='Your cryptography version does not support Ed448')
 
     def _generate_private_key_data(self):
+        format = cryptography.hazmat.primitives.serialization.PrivateFormat.TraditionalOpenSSL
         try:
             if self.type == 'RSA':
                 self.privatekey = cryptography.hazmat.primitives.asymmetric.rsa.generate_private_key(
@@ -487,14 +497,18 @@ class PrivateKeyCryptography(PrivateKeyBase):
                     key_size=self.size,
                     backend=self.cryptography_backend
                 )
-            if CRYPTOGRAPHY_HAS_X25519 and self.type == 'X25519':
+            if CRYPTOGRAPHY_HAS_X25519_FULL and self.type == 'X25519':
                 self.privatekey = cryptography.hazmat.primitives.asymmetric.x25519.X25519PrivateKey.generate()
+                format = cryptography.hazmat.primitives.serialization.PrivateFormat.PKCS8
             if CRYPTOGRAPHY_HAS_X448 and self.type == 'X448':
                 self.privatekey = cryptography.hazmat.primitives.asymmetric.x448.X448PrivateKey.generate()
+                format = cryptography.hazmat.primitives.serialization.PrivateFormat.PKCS8
             if CRYPTOGRAPHY_HAS_ED25519 and self.type == 'Ed25519':
                 self.privatekey = cryptography.hazmat.primitives.asymmetric.ed25519.Ed25519PrivateKey.generate()
+                format = cryptography.hazmat.primitives.serialization.PrivateFormat.PKCS8
             if CRYPTOGRAPHY_HAS_ED448 and self.type == 'Ed448':
                 self.privatekey = cryptography.hazmat.primitives.asymmetric.ed448.Ed448PrivateKey.generate()
+                format = cryptography.hazmat.primitives.serialization.PrivateFormat.PKCS8
             if self.type == 'ECC' and self.curve in self.curves:
                 if self.curves[self.curve]['deprecated']:
                     self.module.warn('Elliptic curves of type {0} should not be used for new keys!'.format(self.curve))
@@ -516,7 +530,7 @@ class PrivateKeyCryptography(PrivateKeyBase):
         # Serialize key
         return self.privatekey.private_bytes(
             encoding=cryptography.hazmat.primitives.serialization.Encoding.PEM,
-            format=cryptography.hazmat.primitives.serialization.PrivateFormat.TraditionalOpenSSL,
+            format=format,
             encryption_algorithm=encryption_algorithm
         )
 
@@ -565,6 +579,10 @@ class PrivateKeyCryptography(PrivateKeyBase):
             return self.type == 'X25519'
         if CRYPTOGRAPHY_HAS_X448 and isinstance(privatekey, cryptography.hazmat.primitives.asymmetric.x448.X448PrivateKey):
             return self.type == 'X448'
+        if CRYPTOGRAPHY_HAS_ED25519 and isinstance(privatekey, cryptography.hazmat.primitives.asymmetric.ed25519.Ed25519PrivateKey):
+            return self.type == 'Ed25519'
+        if CRYPTOGRAPHY_HAS_ED448 and isinstance(privatekey, cryptography.hazmat.primitives.asymmetric.ed448.Ed448PrivateKey):
+            return self.type == 'Ed448'
         if isinstance(privatekey, cryptography.hazmat.primitives.asymmetric.ec.EllipticCurvePrivateKey):
             if self.type != 'ECC':
                 return False
@@ -590,10 +608,7 @@ def main():
             state=dict(type='str', default='present', choices=['present', 'absent']),
             size=dict(type='int', default=4096),
             type=dict(type='str', default='RSA', choices=[
-                'RSA', 'DSA', 'ECC',
-                # FIXME: NO LONGER TRUE: x25519 is missing serialization functions: https://github.com/pyca/cryptography/issues/4386
-                # FIXME: NO LONGER TRUE: x448 is also missing it: https://github.com/pyca/cryptography/pull/4580#issuecomment-437913340
-                # 'X448', 'X25519', 'Ed448', 'Ed25519'
+                'DSA', 'ECC', 'Ed25519', 'Ed448', 'RSA', 'X25519', 'X448'
             ]),
             curve=dict(type='str', choices=[
                 'secp384r1', 'secp521r1', 'secp224r1', 'secp192r1', 'secp256k1',
diff --git a/test/integration/targets/openssl_privatekey/tasks/impl.yml b/test/integration/targets/openssl_privatekey/tasks/impl.yml
index a5128451f7c..86f444615a1 100644
--- a/test/integration/targets/openssl_privatekey/tasks/impl.yml
+++ b/test/integration/targets/openssl_privatekey/tasks/impl.yml
@@ -55,10 +55,6 @@
   when: select_crypto_backend == 'pyopenssl'
 - set_fact:
     ecc_types:
-    # - curve: X448
-    #   min_cryptography_version: "2.5"
-    # - curve: X25519
-    #   min_cryptography_version: "2.0"
     - curve: secp384r1
       openssl_name: secp384r1
       min_cryptography_version: "0.5"
@@ -143,6 +139,41 @@
     label: "{{ item.curve }}"
   register: privatekey_ecc_idempotency
 
+- block:
+  - name: Test other type generation
+    openssl_privatekey:
+      path: '{{ output_dir }}/privatekey-{{ item.type }}.pem'
+      type: "{{ item.type }}"
+      select_crypto_backend: '{{ select_crypto_backend }}'
+    when: cryptography_version.stdout is version(item.min_version, '>=')
+    loop: "{{ types }}"
+    loop_control:
+      label: "{{ item.type }}"
+    register: privatekey_t1_generate
+
+  - name: Test other type generation (idempotency)
+    openssl_privatekey:
+      path: '{{ output_dir }}/privatekey-{{ item.type }}.pem'
+      type: "{{ item.type }}"
+      select_crypto_backend: '{{ select_crypto_backend }}'
+    when: cryptography_version.stdout is version(item.min_version, '>=')
+    loop: "{{ types }}"
+    loop_control:
+      label: "{{ item.type }}"
+    register: privatekey_t1_idempotency
+
+  when: select_crypto_backend == 'cryptography'
+  vars:
+    types:
+      - type: X25519
+        min_version: '2.5'
+      - type: Ed25519
+        min_version: '2.6'
+      - type: Ed448
+        min_version: '2.6'
+      - type: X448
+        min_version: '2.6'
+
 - name: Generate privatekey with passphrase
   openssl_privatekey:
     path: '{{ output_dir }}/privatekeypw.pem'
diff --git a/test/integration/targets/openssl_privatekey/tests/validate.yml b/test/integration/targets/openssl_privatekey/tests/validate.yml
index 7bb1fe454e6..c7762173282 100644
--- a/test/integration/targets/openssl_privatekey/tests/validate.yml
+++ b/test/integration/targets/openssl_privatekey/tests/validate.yml
@@ -105,6 +105,25 @@
   loop_control:
     label: "{{ item.item.curve }}"
 
+- name: Validate other type generation (just check changed)
+  assert:
+    that:
+    - item is changed
+  loop: "{{ privatekey_t1_generate.results }}"
+  when: "'skip_reason' not in item"
+  loop_control:
+    label: "{{ item.item.type }}"
+
+
+- name: Validate other type generation idempotency
+  assert:
+    that:
+    - item is not changed
+  loop: "{{ privatekey_t1_idempotency.results }}"
+  when: "'skip_reason' not in item"
+  loop_control:
+    label: "{{ item.item.type }}"
+
 - name: Validate passphrase changing
   assert:
     that: