Newspaper reports suggest he will move north to play with Glasgow next season.
The 25-year-old Hamilton has made eight starts and seven appearances from the bench this season, and starts for the Falcons in Sunday's Zurich Premiership match at NEC Harlequins.
Newcastle's director of rugby, Rob Andrew, said: "We have been talking with Craig for some time now, and he has aspirations to get back involved with the his national squad after touring with them in the summer, which will be best achieved by a move to Scotland.
"He has been a great servant for us during his time at the club after coming through the academy, and although he still had a year left on his contract we have agreed for him to return home and wish him well."