The Swedish international had been expected to make the switch after failing to agree a deal with the Trotters and left the club last week.
The Turkish club released a statement on Monday, which reads: "Galatasaray Sports Club has announced the official signing of Johan Elmander from Bolton Wanderers on Monday.
"Elmander has signed a contract valid until the end of 2013-14 football season."
Bolton captain Kevin Davies has paid tribute to his former team-mate, who scored 12 times in 50 appearances in the 2010-11 season.
He told Bolton News: "I'm not too sure how he found his time here, whether he had a happy time or not. But this season he's been asked to play in numerous positions and he always gave his all.
"His stats are always really high and he's scored a few good goals. It hasn't quite worked out for him but then I've been on a big move like that and it hasn't quite worked out.
"He's a great lad and the gaffer speaks very highly of him because of his work ethic and what he brought to us, so we wish him well."