The Chelsea legend has long been linked with a return to Europe after leaving Stamford Bridge for China in the summer, and, despite rumors of interest from Italy, the Turkish champions have won the race for his signature.
"Big clubs can reach for higher targets with bigger goals," team president Unal Aysal said.
"Drogba said that he was very happy to play for a big club like Galatasaray in the future. Drogba met our coach and decided to come to Galatasaray."
The Cote d'Ivoire icon will earn 2 million euros for the remainder of the 2012-13 season, and 4 million euros for the duration of the 2013-14 campaign, with an additional bonus of 15,000 euros for each match he plays.
Both AC Milan and Juventus had been closely linked with a January move for Drogba, but Gala announced yesterday that it had opened talks with the player.
He will link up with his new teammates once Cote d'Ivoire's involvement at the Africa Cup of Nations ends.
Galatasaray has been one of the most active teams during the Janaury window so far. Wesley Sneijder completed a move from Inter to Galatasaray last week for a transfer fee believed to be in the region of 10 million euros.