The 33-year-old Frenchman underwent his medical on Wednesday and has now signed a two-year deal with the Super Lig club.
Malouda, who has made 80 appearances for his country, was prolific for Chelsea in the 2010-11 season, in which he scored 13 goals in 38 league appearances, but a poor follow-up campaign saw him fall out of favour.
The midfielder was limited largely to cup appearances under Roberto Di Matteo last term and was unable to force his way back into the plans of replacement Rafa Benitez.
Malouda was released at the end of the season, but left Stamford Bridge having won the Premier League title and three FA Cup winners' medals.
The switch to the Turkish top flight marks the fourth move of his senior career, which began at French side Chateauroux in 1996.
Malouda has also enjoyed spells at Guingamp and Lyon in his homeland.
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