The 24-year-old, who has been on loan at the Bhoys for two consecutive seasons, rejected interest from elsewhere to sign a four-year deal at Parkhead.
And the ex-Newcastle United stopper is delighted at guaranteed first-team football as well as the chance to star in the Champions League.
He told reporters: “Celtic as a football club speaks for itself.
“We have got the chance to play in Europe again which I'm delighted about. With the size of the club and the European chance, it was too good to turn down.
“Not many keepers get the chance to play in Europe.
“We did well last season as a squad so there was a bit of interest elsewhere but I always knew I would be back here.
“I think this is the right move at this point. I've progressed a lot in the last few years, it's important I keep doing that and keep playing first-team football.”
|KINGS OF EUROPE
|250/1||Celtic are 250/1 with Bet365 to win the Champions League next season|
Forster is not put off by Old Firm rivals Rangers newco’s absence from the Scottish Premier League next season after it was announced that 10 SPL clubs had voted against their application to join the league.
“Obviously the Old Firm games were big games but every game is a challenge in its own way. That, combined with Europe, should make for a good season,” he said.
“They were a big part of the SPL. But you have just got to look at the positives and move on.”