diff --git a/src/fastmcp/client/transports.py b/src/fastmcp/client/transports.py
index cd565bbf59..2eaede2a1b 100644
--- a/src/fastmcp/client/transports.py
+++ b/src/fastmcp/client/transports.py
@@ -23,7 +23,7 @@
 )
 from mcp.client.sse import sse_client
 from mcp.client.stdio import stdio_client
-from mcp.client.streamable_http import streamablehttp_client
+from mcp.client.streamable_http import streamable_http_client
 from mcp.server.fastmcp import FastMCP as FastMCP1Server
 from mcp.shared._httpx_utils import McpHttpClientFactory
 from mcp.shared.memory import create_client_server_memory_streams
@@ -252,6 +252,16 @@ def __init__(
         self.httpx_client_factory = httpx_client_factory
         self._set_auth(auth)
 
+        if sse_read_timeout is not None:
+            if fastmcp.settings.deprecation_warnings:
+                warnings.warn(
+                    "The `sse_read_timeout` parameter is deprecated and no longer used. "
+                    "The new streamable_http_client API does not support this parameter. "
+                    "Use `read_timeout_seconds` in session_kwargs or configure timeout on "
+                    "the httpx client via `httpx_client_factory` instead.",
+                    DeprecationWarning,
+                    stacklevel=2,
+                )
         if isinstance(sse_read_timeout, int | float):
             sse_read_timeout = datetime.timedelta(seconds=float(sse_read_timeout))
         self.sse_read_timeout = sse_read_timeout
@@ -269,28 +279,36 @@ def _set_auth(self, auth: httpx.Auth | Literal["oauth"] | str | None):
     async def connect_session(
         self, **session_kwargs: Unpack[SessionKwargs]
     ) -> AsyncIterator[ClientSession]:
-        client_kwargs: dict[str, Any] = {}
-
-        # load headers from an active HTTP request, if available. This will only be true
+        # Load headers from an active HTTP request, if available. This will only be true
         # if the client is used in a FastMCP Proxy, in which case the MCP client headers
         # need to be forwarded to the remote server.
-        client_kwargs["headers"] = get_http_headers() | self.headers
+        headers = get_http_headers() | self.headers
 
-        # sse_read_timeout has a default value set, so we can't pass None without overriding it
-        # instead we simply leave the kwarg out if it's not provided
-        if self.sse_read_timeout is not None:
-            client_kwargs["sse_read_timeout"] = self.sse_read_timeout
+        # Build httpx client configuration
+        httpx_client_kwargs: dict[str, Any] = {
+            "headers": headers,
+            "auth": self.auth,
+            "follow_redirects": True,
+        }
+
+        # Configure timeout if provided (convert timedelta to seconds for httpx)
         if session_kwargs.get("read_timeout_seconds") is not None:
-            client_kwargs["timeout"] = session_kwargs.get("read_timeout_seconds")
+            read_timeout_seconds = cast(
+                datetime.timedelta, session_kwargs.get("read_timeout_seconds")
+            )
+            httpx_client_kwargs["timeout"] = read_timeout_seconds.total_seconds()
 
+        # Create httpx client from factory or use default
         if self.httpx_client_factory is not None:
-            client_kwargs["httpx_client_factory"] = self.httpx_client_factory
+            http_client = self.httpx_client_factory(**httpx_client_kwargs)
+        else:
+            http_client = httpx.AsyncClient(**httpx_client_kwargs)
 
-        async with streamablehttp_client(
-            self.url,
-            auth=self.auth,
-            **client_kwargs,
-        ) as transport:
+        # Ensure httpx client is closed after use
+        async with (
+            http_client,
+            streamable_http_client(self.url, http_client=http_client) as transport,
+        ):
             read_stream, write_stream, get_session_id = transport
             self._get_session_id_cb = get_session_id
             async with ClientSession(