The 39-year-old began his coaching journey with United's Academy between 2005 and 2007 and returned in August 2022 after 15 years with the Football Association.
The club thanks Graeme for his service and wishes him the best for the future.
Steve Harper, Newcastle United's Academy Director, said: "I would like to thank Graeme for his excellent work in developing our young players both on and off the pitch.
"Whenever a player of staff member moves on to first team opportunities, whether it's here or elsewhere, we can all be very proud of them.
"Middlesbrough are getting a great guy, a very good coach and we all wish him every success with his new role.
"The search for a new Under-18s lead coach has already begun."