The 34-year-old - looking to complete his disputed move from Shanghai Shenhua - flew in from the African Nations Cup, where he had been playing for the Ivory Coast until their defeat against Nigeria.
And he was greeted by hundreds of fans at the airport.
"I'm very happy to be here for me as it's a new adventure, a new part of my life," he told the club's website. "I will do my best to be successful for the club."
Drogba has agreed an 18-month deal with the big-spending Turkish club, who signed Wesley Sneijder from Inter Milan last month.
However, his former club Shenhua Shanghai have said they will challenge the deal, insisting Drogba remains under contract with them.
Drogba moved to Shanghai on a reported two-and-a-half-year deal last summer, but his camp claimed the deal had become invalid.
Last month Nicolas Anelka, who had also joined Shanghai from Chelsea, returned to Europe by joining Juventus.