Drogba joined the Istanbul outfit from Chinese club Shanghai Shenhua last January and helped them to the Super Lig title and the Turkish Super Cup.
The 36-year-old has been linked with a move back to Chelsea, potentially in a player-coach role, but he offered no further insight into his future while bidding farewell to the Galatasaray fans.
"Galatasaray will always be in my heart. I'm very proud to have represented this team. I didn't come here for money. If I wanted money I would have stayed in China," Drogba told the club's official TV channel.
"I came to Turkey to play football, to feel the passion again. Scoring against Fenerbahce and Besiktas, I think I gave some happiness to our fans."
Drogba, who will feature for Ivory Coast in this summer's World Cup, was unable to fire Galatasaray to the league title this season as they finished second in the table, nine points behind champions Fenerbahce.