Forster, 24, has spent the past two seasons on loan at Celtic Park but has now signed a four-year contract with the SPL champions.
He made 33 starts in the SPL last season as Celtic finished 20 points clear of Rangers.
"This is a massive club and I feel like this is a step forward in my career," he told the club's official website. "I want to win things as a team and improve as an individual and I think I will be able to do that at Celtic.
"It also gives me a great opportunity to play in the Champions League if we get through the qualifiers. I really enjoyed my time in Europe last season so I will be looking forward to it if it happens again.
"I enjoyed last season as a whole and we have a great young squad here. The players and the coaches make it an enjoyable place to be and I like being a part of this team."
Neil Lennon added: "We are delighted that Fraser has committed his future to the club and we believe he will be a magnificent addition to the squad. He gives us that continuity so this is something we are really pleased about. He is a top-class keeper."