diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index e67381fb..be10c2ba 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -26,6 +26,7 @@ Added
 - Add missing exceptions.InvalidKeyError to jwt module __init__ imports `#620 <https://github.com/jpadilla/pyjwt/pull/620>`__
 - Add support for ES256K algorithm `#629 <https://github.com/jpadilla/pyjwt/pull/629>`__
 - Add `from_jwk()` to Ed25519Algorithm `#621 <https://github.com/jpadilla/pyjwt/pull/621>`__
+- Add `to_jwk()` to Ed25519Algorithm `#643 <https://github.com/jpadilla/pyjwt/pull/643>`__
 
 `v2.0.1 <https://github.com/jpadilla/pyjwt/compare/2.0.0...2.0.1>`__
 --------------------------------------------------------------------
diff --git a/jwt/algorithms.py b/jwt/algorithms.py
index 50719bea..42648ce3 100644
--- a/jwt/algorithms.py
+++ b/jwt/algorithms.py
@@ -37,6 +37,10 @@
         rsa_recover_prime_factors,
     )
     from cryptography.hazmat.primitives.serialization import (
+        Encoding,
+        NoEncryption,
+        PrivateFormat,
+        PublicFormat,
         load_pem_private_key,
         load_pem_public_key,
         load_ssh_public_key,
@@ -587,6 +591,45 @@ def verify(self, msg, key, sig):
             except cryptography.exceptions.InvalidSignature:
                 return False
 
+        @staticmethod
+        def to_jwk(key):
+            if isinstance(key, Ed25519PublicKey):
+                x = key.public_bytes(
+                    encoding=Encoding.Raw,
+                    format=PublicFormat.Raw,
+                )
+
+                return json.dumps(
+                    {
+                        "x": base64url_encode(force_bytes(x)).decode(),
+                        "kty": "OKP",
+                        "crv": "Ed25519",
+                    }
+                )
+
+            if isinstance(key, Ed25519PrivateKey):
+                d = key.private_bytes(
+                    encoding=Encoding.Raw,
+                    format=PrivateFormat.Raw,
+                    encryption_algorithm=NoEncryption(),
+                )
+
+                x = key.public_key().public_bytes(
+                    encoding=Encoding.Raw,
+                    format=PublicFormat.Raw,
+                )
+
+                return json.dumps(
+                    {
+                        "x": base64url_encode(force_bytes(x)).decode(),
+                        "d": base64url_encode(force_bytes(d)).decode(),
+                        "kty": "OKP",
+                        "crv": "Ed25519",
+                    }
+                )
+
+            raise InvalidKeyError("Not a public or private key")
+
         @staticmethod
         def from_jwk(jwk):
             try:
diff --git a/tests/test_algorithms.py b/tests/test_algorithms.py
index 2144d484..0ece6d88 100644
--- a/tests/test_algorithms.py
+++ b/tests/test_algorithms.py
@@ -800,3 +800,28 @@ def test_ed25519_jwk_fails_on_invalid_json(self):
         v["d"] = "123"
         with pytest.raises(InvalidKeyError):
             algo.from_jwk(v)
+
+    def test_ed25519_to_jwk_works_with_from_jwk(self):
+        algo = Ed25519Algorithm()
+
+        with open(key_path("jwk_okp_key_Ed25519.json")) as keyfile:
+            priv_key_1 = algo.from_jwk(keyfile.read())
+
+        with open(key_path("jwk_okp_pub_Ed25519.json")) as keyfile:
+            pub_key_1 = algo.from_jwk(keyfile.read())
+
+        pub = algo.to_jwk(pub_key_1)
+        pub_key_2 = algo.from_jwk(pub)
+        pri = algo.to_jwk(priv_key_1)
+        priv_key_2 = algo.from_jwk(pri)
+
+        signature_1 = algo.sign(b"Hello World!", priv_key_1)
+        signature_2 = algo.sign(b"Hello World!", priv_key_2)
+        assert algo.verify(b"Hello World!", pub_key_2, signature_1)
+        assert algo.verify(b"Hello World!", pub_key_2, signature_2)
+
+    def test_ed25519_to_jwk_raises_exception_on_invalid_key(self):
+        algo = Ed25519Algorithm()
+
+        with pytest.raises(InvalidKeyError):
+            algo.to_jwk({"not": "a valid key"})