The 24-year old goalkeeper has spent the past two seasons on loan with the Scottish champions and has now penned a four-year deal to move to Glasgow on a permanent basis.
Forster, who has made over 70 appearances for the Hoops, was set to battle with the likes of Tim Krul, Rob Eliot and Steve Harper for the number one shirt with the Magpies so has decided to move on to become a concrete fixture at Parkhead.
"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."