Carlisle - where the 21-year-old spent last season on loan - were also interested, but Green sees his future at the Kingston Communications Stadium.
He said: "I'm glad everything has been sorted out. It's what I wanted. Don't get me wrong, I would have stayed at Newcastle because I wanted to play in the Premiership.
"Outside the Premiership, though, I don't think there are too many better places than here."
Green celebrated signing the three-year deal with a goal against Hartlepool yesterday, but said that the three points was the most important thing.