A move for the 23-year-old has been mooted throughout the week and the Scottish Premiership champions confirmed it on Saturday morning.
He started his career with FC KooTeePee before moving to Spain with Sevilla and Sevilla Atletico.
A spell with HJK back in Finland followed before he headed to Schalke in 2011, having impressed the German side while playing against them for HJK.
The Parkhead club have been angered by attempts to lure the Englishman, who was this week named in Roy Hodgson's squad for the Three Lions upcoming World Cup qualifiers with Moldova and Ukraine.
Forster has already been heavily linked with a move to Benfica, but Hoops boss Neil Lennon sees the former Newcastle stopper as integral to his plans for the club's Champions League clashes with AC Milan, Barcelona and Ajax.
The 25-year-old was a key figure in last year's run to the last 16 in the competition and Lennon insists Foster is going nowhere.
The Celtic manager told the Scottish Daily Mail: ''Fraser's not for sale. We had no confirmed bids for him. We have actually written a letter to one club, just warning them off basically.''
A left-back is also on Lennon's wanted list and a successful pursuit would take the number of summer signings Lennon has made to seven after the captures of Amido Balde, Virgil van Dijk, Derk Boerrigter and Steven Mouyokolo.
But the Celtic boss admits adding to his squad has been a frustrating process.
''We've been looking everywhere, all over the world, really - South America, Canada, places like that and sometimes it's very difficult to do deals,'' he said.
''Sometimes you think you're there and then the price goes up, another agent gets involved and you end up talking to three different agents. It just becomes a bit of a muddle.
''We do our business cleanly, simply and quickly, but sometimes that can't be the case. I think there's money there to spend, it's just about trying to get the right player in for the right price.''