He agreed the permanent switch over the weekend.
Forster, who had been trailed by West Ham, QPR and Southampton, told the Scottish Sun: "After winning the league it was the right decision for me to come back to Celtic. The opportunity to play in the Champions League was something I couldn't turn down. I'm excited about that.
"I was never tempted by other possibilities. There's always speculation, but in my mind I felt I'd end up back at Celtic.
"I'm very happy that I'm going to be at Celtic for the next four years at least.
"We won the league last season and it's important we aim to keep on improving, individually and collectively."