diff --git a/.changeset/fix-transport-exact-optional-property-types.md b/.changeset/fix-transport-exact-optional-property-types.md
new file mode 100644
index 0000000000..db0b4266b4
--- /dev/null
+++ b/.changeset/fix-transport-exact-optional-property-types.md
@@ -0,0 +1,10 @@
+---
+'@modelcontextprotocol/sdk': patch
+---
+
+Add explicit `| undefined` to the optional properties of the `Transport` interface (`onclose`, `onerror`, `onmessage`, `sessionId`).
+
+Under `exactOptionalPropertyTypes: true`, `onclose?: () => void` means the property may be absent but never explicitly `undefined`. The concrete transports declare these members as accessors typed `(() => void) | undefined`, so the SDK's own transports were not assignable to the
+SDK's own `Transport` interface, and `server.connect(new StreamableHTTPServerTransport(...))` failed with TS2379. Consumers had to either cast at the call site or disable the flag for their whole project.
+
+This is a backport of the same fix already merged on `main` in #1766, and resolves #2083 for the v1 line.
diff --git a/src/shared/transport.ts b/src/shared/transport.ts
index f9b21bed32..447a379434 100644
--- a/src/shared/transport.ts
+++ b/src/shared/transport.ts
@@ -98,14 +98,14 @@ export interface Transport {
      *
      * This should be invoked when close() is called as well.
      */
-    onclose?: () => void;
+    onclose?: (() => void) | undefined;
 
     /**
      * Callback for when an error occurs.
      *
      * Note that errors are not necessarily fatal; they are used for reporting any kind of exceptional condition out of band.
      */
-    onerror?: (error: Error) => void;
+    onerror?: ((error: Error) => void) | undefined;
 
     /**
      * Callback for when a message (request or response) is received over the connection.
@@ -114,12 +114,12 @@ export interface Transport {
      *
      * The requestInfo can be used to get the original request information (headers, etc.)
      */
-    onmessage?: <T extends JSONRPCMessage>(message: T, extra?: MessageExtraInfo) => void;
+    onmessage?: (<T extends JSONRPCMessage>(message: T, extra?: MessageExtraInfo) => void) | undefined;
 
     /**
      * The session ID generated for this connection.
      */
-    sessionId?: string;
+    sessionId?: string | undefined;
 
     /**
      * Sets the protocol version used for the connection (called when the initialize response is received).