Methods and apparatus to migrate border gateway protocol sessions between routers are disclosed. An example method to migrate a border gateway protocol session from a first router to a second router disclosed herein comprises exporting a connection state to migrate a transport control protocol connection supporting the border gateway protocol session with a session endpoint from the first router to the second router, and after the transport control protocol connection has been migrated to the second router, announcing, from the first router to the second router, routes contained in an exported routing information base associated with the session endpoint, the second router to process the routes to migrate handling of the border gateway protocol session with the session endpoint to the second router.