Gutierrez played almost 200 games for the Magpies after joining the club five and a half years ago, but has not started a game since the opening day of the season.
He said: “It wasn’t my decision to leave Newcastle and it was an honour to play for them.”
Hughton added: “Jonas has been in England for five years, so there won’t be that settling in period that you would have with some other players – and that is important.”