diff --git a/moto/rds/models.py b/moto/rds/models.py
index c4825b6a9292..8aae7e86d4aa 100644
--- a/moto/rds/models.py
+++ b/moto/rds/models.py
@@ -1890,6 +1890,10 @@ def copy_db_snapshot(
         tags: Optional[List[Dict[str, str]]] = None,
         copy_tags: bool = False,
     ) -> DBSnapshot:
+        if source_snapshot_identifier.startswith("arn:aws:rds:"):
+            source_snapshot_identifier = self.extract_snapshot_name_from_arn(
+                source_snapshot_identifier
+            )
         if source_snapshot_identifier not in self.database_snapshots:
             raise DBSnapshotNotFoundError(source_snapshot_identifier)
 
@@ -2010,9 +2014,28 @@ def modify_db_instance(
     def reboot_db_instance(self, db_instance_identifier: str) -> DBInstance:
         return self.describe_db_instances(db_instance_identifier)[0]
 
+    def extract_snapshot_name_from_arn(self, snapshot_arn: str) -> str:
+        arn_breakdown = snapshot_arn.split(":")
+        region_name, account_id, resource_type, snapshot_name = arn_breakdown[3:7]
+        if resource_type != "snapshot":
+            raise InvalidParameterValue(
+                "The parameter SourceDBSnapshotIdentifier is not a valid identifier. "
+                "Identifiers must begin with a letter; must contain only ASCII "
+                "letters, digits, and hyphens; and must not end with a hyphen or "
+                "contain two consecutive hyphens."
+            )
+        if region_name != self.region_name or account_id != self.account_id:
+            raise NotImplementedError(
+                "Cross account/region snapshot handling is not yet implemented in moto."
+            )
+        return snapshot_name
+
     def restore_db_instance_from_db_snapshot(
         self, from_snapshot_id: str, overrides: Dict[str, Any]
     ) -> DBInstance:
+        if from_snapshot_id.startswith("arn:aws:rds:"):
+            from_snapshot_id = self.extract_snapshot_name_from_arn(from_snapshot_id)
+
         snapshot = self.describe_db_snapshots(
             db_instance_identifier=None, db_snapshot_identifier=from_snapshot_id
         )[0]
diff --git a/tests/test_rds/test_rds.py b/tests/test_rds/test_rds.py
index 2c7fc5fd1ee4..36dddcadffc4 100644
--- a/tests/test_rds/test_rds.py
+++ b/tests/test_rds/test_rds.py
@@ -1141,8 +1141,13 @@ def test_create_db_snapshots_with_tags():
 
 
 @pytest.mark.parametrize("delete_db_instance", [True, False])
+@pytest.mark.parametrize(
+    "db_snapshot_identifier",
+    ("snapshot-1", f"arn:aws:rds:{DEFAULT_REGION}:123456789012:snapshot:snapshot-1"),
+    ids=("by_name", "by_arn"),
+)
 @mock_aws
-def test_copy_db_snapshots(delete_db_instance: bool):
+def test_copy_db_snapshots(delete_db_instance: bool, db_snapshot_identifier: str):
     conn = boto3.client("rds", region_name=DEFAULT_REGION)
 
     conn.create_db_instance(
@@ -1166,7 +1171,8 @@ def test_copy_db_snapshots(delete_db_instance: bool):
         conn.delete_db_instance(DBInstanceIdentifier="db-primary-1")
 
     target_snapshot = conn.copy_db_snapshot(
-        SourceDBSnapshotIdentifier="snapshot-1", TargetDBSnapshotIdentifier="snapshot-2"
+        SourceDBSnapshotIdentifier=db_snapshot_identifier,
+        TargetDBSnapshotIdentifier="snapshot-2",
     ).get("DBSnapshot")
 
     assert target_snapshot.get("Engine") == "postgres"
@@ -1176,6 +1182,21 @@ def test_copy_db_snapshots(delete_db_instance: bool):
     assert result["TagList"] == []
 
 
+@mock_aws
+def test_copy_db_snapshot_invalid_arns():
+    conn = boto3.client("rds", region_name=DEFAULT_REGION)
+
+    invalid_arn = (
+        f"arn:aws:rds:{DEFAULT_REGION}:123456789012:this-is-not-a-snapshot:snapshot-1"
+    )
+    with pytest.raises(ClientError) as ex:
+        conn.copy_db_snapshot(
+            SourceDBSnapshotIdentifier=invalid_arn,
+            TargetDBSnapshotIdentifier="snapshot-2",
+        )
+    assert "is not a valid identifier" in ex.value.response["Error"]["Message"]
+
+
 original_snapshot_tags = [{"Key": "original", "Value": "snapshot tags"}]
 new_snapshot_tags = [{"Key": "new", "Value": "tag"}]
 
@@ -1321,11 +1342,18 @@ def test_delete_db_snapshot():
         conn.describe_db_snapshots(DBSnapshotIdentifier="snapshot-1")
 
 
+@pytest.mark.parametrize(
+    "db_snapshot_identifier",
+    ("snapshot-1", f"arn:aws:rds:{DEFAULT_REGION}:123456789012:snapshot:snapshot-1"),
+    ids=("by_name", "by_arn"),
+)
 @pytest.mark.parametrize(
     "custom_db_subnet_group", [True, False], ids=("custom_subnet", "default_subnet")
 )
 @mock_aws
-def test_restore_db_instance_from_db_snapshot(custom_db_subnet_group: bool):
+def test_restore_db_instance_from_db_snapshot(
+    db_snapshot_identifier: str, custom_db_subnet_group: bool
+):
     conn = boto3.client("rds", region_name=DEFAULT_REGION)
     conn.create_db_instance(
         DBInstanceIdentifier="db-primary-1",
@@ -1353,9 +1381,12 @@ def test_restore_db_instance_from_db_snapshot(custom_db_subnet_group: bool):
         )
 
     # restore
+    new_instance = conn.restore_db_instance_from_db_snapshot(
+        DBInstanceIdentifier="db-restore-1", DBSnapshotIdentifier=db_snapshot_identifier
+    )["DBInstance"]
     kwargs = {
         "DBInstanceIdentifier": "db-restore-1",
-        "DBSnapshotIdentifier": "snapshot-1",
+        "DBSnapshotIdentifier": db_snapshot_identifier,
     }
     if custom_db_subnet_group:
         kwargs["DBSubnetGroupName"] = "custom-subnet-group"