The former Chelsea striker, 36, moved to Istanbul in January last year and helped Galatasaray win the Super Lig title and Turkish Super Cup.
However, he will now seek a move elsewhere after bringing down the curtain on his time in Turkey.
"Galatasaray will always be in my heart," Drogba told the club's official TV channel. "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 (where he played for Shanghai Shenhua).
"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."
Galatasaray finished second in the Turkish Super Lig this season, nine points behind champions Fenerbahce.
Drogba is set to be a key member of Ivory Coast's squad at the FIFA World Cup.
