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..9b735ff1cd
--- /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`, `setProtocolVersion`) and of `TransportSendOptions` (`relatedRequestId`, `resumptionToken`, `onresumptiontoken`).
+
+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 09fe611722..2be18ae85b 100644
--- a/src/shared/transport.ts
+++ b/src/shared/transport.ts
@@ -143,21 +143,21 @@ export type TransportSendOptions = {
     /**
      * If present, `relatedRequestId` is used to indicate to the transport which incoming request to associate this outgoing message with.
      */
-    relatedRequestId?: RequestId;
+    relatedRequestId?: RequestId | undefined;
 
     /**
      * The resumption token used to continue long-running requests that were interrupted.
      *
      * This allows clients to reconnect and continue from where they left off, if supported by the transport.
      */
-    resumptionToken?: string;
+    resumptionToken?: string | undefined;
 
     /**
      * A callback that is invoked when the resumption token changes, if supported by the transport.
      *
      * This allows clients to persist the latest token for potential reconnection.
      */
-    onresumptiontoken?: (token: string) => void;
+    onresumptiontoken?: ((token: string) => void) | undefined;
 };
 /**
  * Describes the minimal contract for an MCP transport that a client or server can communicate over.
@@ -189,14 +189,14 @@ 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.
@@ -205,15 +205,15 @@ 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).
      */
-    setProtocolVersion?: (version: string) => void;
+    setProtocolVersion?: ((version: string) => void) | undefined;
 }