diff --git a/elasticsearch_dsl/connections.py b/elasticsearch_dsl/connections.py
index 7bfabeb0..d871c1ac 100644
--- a/elasticsearch_dsl/connections.py
+++ b/elasticsearch_dsl/connections.py
@@ -58,7 +58,7 @@ def add_connection(self, alias, conn):
         """
         Add a connection object, it will be passed through as-is.
         """
-        self._conns[alias] = conn
+        self._conns[alias] = self._with_user_agent(conn)
 
     def remove_connection(self, alias):
         """
@@ -82,7 +82,7 @@ def create_connection(self, alias="default", **kwargs):
         """
         kwargs.setdefault("serializer", serializer)
         conn = self._conns[alias] = self.elasticsearch_class(**kwargs)
-        return conn
+        return self._with_user_agent(conn)
 
     def get_connection(self, alias="default"):
         """
@@ -96,7 +96,7 @@ def get_connection(self, alias="default"):
         # do not check isinstance(Elasticsearch) so that people can wrap their
         # clients
         if not isinstance(alias, str):
-            return alias
+            return self._with_user_agent(alias)
 
         # connection already established
         try:
@@ -111,6 +111,21 @@ def get_connection(self, alias="default"):
             # no connection and no kwargs to set one up
             raise KeyError(f"There is no connection with alias {alias!r}.")
 
+    def _with_user_agent(self, conn):
+        from . import __versionstr__  # this is here to avoid circular imports
+
+        # try to inject our user agent
+        if hasattr(conn, "_headers"):
+            is_frozen = conn._headers.frozen
+            if is_frozen:
+                conn._headers = conn._headers.copy()
+            conn._headers.update(
+                {"user-agent": f"elasticsearch-dsl-py/{__versionstr__}"}
+            )
+            if is_frozen:
+                conn._headers.freeze()
+        return conn
+
 
 connections = Connections()
 configure = connections.configure
diff --git a/tests/test_connections.py b/tests/test_connections.py
index b22e6eba..2b218ce5 100644
--- a/tests/test_connections.py
+++ b/tests/test_connections.py
@@ -107,3 +107,29 @@ def test_create_connection_adds_our_serializer():
 
     c_serializers = c.get_connection("testing").transport.serializers
     assert c_serializers.serializers["application/json"] is serializer.serializer
+
+
+def test_connection_has_correct_user_agent():
+    c = connections.Connections(elasticsearch_class=Elasticsearch)
+
+    c.create_connection("testing", hosts=["https://es.com:9200"])
+    assert (
+        c.get_connection("testing")
+        ._headers["user-agent"]
+        .startswith("elasticsearch-dsl-py/")
+    )
+
+    my_client = Elasticsearch(hosts=["http://localhost:9200"])
+    my_client = my_client.options(headers={"user-agent": "my-user-agent/1.0"})
+    c.add_connection("default", my_client)
+    assert c.get_connection()._headers["user-agent"].startswith("elasticsearch-dsl-py/")
+
+    my_client = Elasticsearch(hosts=["http://localhost:9200"])
+    assert (
+        c.get_connection(my_client)
+        ._headers["user-agent"]
+        .startswith("elasticsearch-dsl-py/")
+    )
+
+    not_a_client = object()
+    assert c.get_connection(not_a_client) == not_a_client