Graham has been United's chief scout for seven years, taking up the position towards the end of the 2009/10 season which saw the club gain promotion back to the Premier League under former manager Chris Hughton.
Graham was instrumental in identifying players from across the UK and Europe, including signings Yohan Cabaye, Matthieu Debuchy, Vurnon Anita, Moussa Sissoko, Papiss Cisse and Cheick Tiote.
Managing Director Lee Charnley said: "It has been my pleasure to work with Graham over the last seven years as both a colleague and a friend. He can count some of Newcastle’s most successful players in recent years as his 'finds'.
"Everyone connected with Newcastle United wishes Graham the very best for the future."
The club is now reviewing its scouting operation and will make an announcement on any further changes in due course.