diff --git a/distributed/scheduler.py b/distributed/scheduler.py
index 445ffd96e8..e79521bc35 100644
--- a/distributed/scheduler.py
+++ b/distributed/scheduler.py
@@ -223,14 +223,24 @@ class ClientState:
     #: Output of :func:`distributed.versions.get_versions` on the client
     versions: dict[str, Any]
 
+    #: Remote address of the client connection as seen by the scheduler.
+    address: str | None
+
     __slots__ = tuple(__annotations__)
 
-    def __init__(self, client: str, *, versions: dict[str, Any] | None = None):
+    def __init__(
+        self,
+        client: str,
+        *,
+        versions: dict[str, Any] | None = None,
+        address: str | None = None,
+    ):
         self.client_key = client
         self._hash = hash(client)
         self.wants_what = set()
         self.last_seen = time()
         self.versions = versions or {}
+        self.address = address
 
     def __hash__(self) -> int:
         return self._hash
@@ -5907,9 +5917,12 @@ async def add_client(
         """
         assert client is not None
         comm.name = "Scheduler->Client"
-        logger.info("Receive client connection: %s", client)
+        client_address = comm.peer_address
+        logger.info("Receive client connection: %s at %s", client, client_address)
         self.log_event(["all", client], {"action": "add-client", "client": client})
-        self.clients[client] = ClientState(client, versions=versions)
+        self.clients[client] = ClientState(
+            client, versions=versions, address=client_address
+        )
         self._client_connections_added_total += 1
 
         for plugin in list(self.plugins.values()):
@@ -5944,15 +5957,24 @@ async def add_client(
                     await self.client_comms[client].close()
                     del self.client_comms[client]
                     if self.status == Status.running:
-                        logger.info("Close client connection: %s", client)
+                        logger.info(
+                            "Close client connection: %s at %s",
+                            client,
+                            client_address,
+                        )
             except TypeError:  # comm becomes None during GC
                 pass
 
     def remove_client(self, client: str, stimulus_id: str | None = None) -> None:
         """Remove client from network"""
         stimulus_id = stimulus_id or f"remove-client-{time()}"
+        client_state = self.clients.get(client)
+        client_address = client_state.address if client_state is not None else None
         if self.status == Status.running:
-            logger.info("Remove client %s", client)
+            if client_address is not None:
+                logger.info("Remove client %s at %s", client, client_address)
+            else:
+                logger.info("Remove client %s", client)
         self.log_event(["all", client], {"action": "remove-client", "client": client})
         try:
             cs: ClientState = self.clients[client]
diff --git a/distributed/tests/test_scheduler.py b/distributed/tests/test_scheduler.py
index ff4d4268d2..ad1073be17 100644
--- a/distributed/tests/test_scheduler.py
+++ b/distributed/tests/test_scheduler.py
@@ -878,6 +878,18 @@ async def test_clear_events_client_removal(c, s, a, b):
         assert time() < start + 2
 
 
+@gen_cluster(nthreads=[])
+async def test_client_connection_logs_include_address(s):
+    with captured_logger("distributed.scheduler", level=logging.INFO) as caplog:
+        async with Client(s.address, asynchronous=True) as c:
+            client_id = c.id
+
+    logs = caplog.getvalue()
+    assert f"Receive client connection: {client_id} at " in logs
+    assert f"Remove client {client_id} at " in logs
+    assert f"Close client connection: {client_id} at " in logs
+
+
 @gen_cluster(client=True, nthreads=[])
 async def test_add_worker(c, s):
     x = c.submit(inc, 1, key="x")