Carrick is joining brother Michael Carrick's coaching staff at Middlesbrough.
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Steve Harper, Newcastle United's Academy Director, told the club's website: "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."