The former Chelsea star has made the move to Turkey from Shanghai Shenhua after months of speculation linking him with a move away from the Chinese Super League
The Chelsea legend has long been linked with a return to Europe after leaving Stamford Bridge for China in the summer, and, despite rumours of interest from Italy, the Turkish champions have won the race for his signature.
"Big clubs can reach for higher targets with bigger goals," the club's president Unal Aysal commented on the deal.
"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."
On Twitter, Drogba told his PR company: "The opportunity to play for this great club was an offer that I could not turn down.
"I am looking forward to playing in the Champions League again, against the best clubs in Europe."
The Cote d'Ivoire icon will earn €2 million for the remainder of the 2012-13 season, and €4m for the duration of the 2013-14 campaign, with an additional bonus of €15,000 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 they had opened talks with the player.
He will link up with his new team-mates once Cote d'Ivoire's involvement at the Africa Cup of Nations ends.
Drogba is the second star name to move to the Turk Telekom Arena this January, with Wesley Sneijder making the switch from Inter to Istanbul last week.