The deal is for 18 months starting in the second half of the current season, Galatasaray Sportif, the Istanbul's club merchandising unit, said.
Cote d'Ivoire's Didier Drogba (L) challenges Tunisia's Aymen Abdennour during their African Nations Cup Group D soccer match in Rustenburg, Jan 26, 2013.
"The opportunity to play for this great club was an offer that I could not turn down," Drogba was quoted as saying on Twitter.
"I am looking forward to playing in the Champions League again, against the best clubs in Europe," added the Cote d'Ivoire captain, who won Europe's leading club competition with Chelsea last year when he scored the decisive penalty in a shootout.
The Galatasaray deal includes transfer fees totalling 6 million euros ($8 million) and payments of 15,000 euros per match, plus signing fees of 4 million euros.
The 34-year-old Drogba, on African Nations Cup duty in South Africa with his country, moved to China after Chelsea's Champions League triumph last year.
Drogba applied for permission to leave on loan before the January transfer window but world soccer's ruling body FIFA refused the request.
Didier Drogba, right, of Shanghai Shenhua goes past a Shandong Luneng player during their Chinese Super League game in Jinan, East China's Shandong province, Aug 25 file photo.
The striker returned to Chelsea to train at his former club in a bid to stay sharp for the Nations Cup, fuelling media speculation of a return to Europe.
Drogba's transfer comes less than a week after Netherlands midfielder and 2010 Champions League winner Wesley Sneijder joined Galatasaray from Inter Milan.
Galatasaray have been drawn to meet German club Schalke 04 in the last 16 of the Champions League next month.
Cote d'Ivoire's Didier Drogba reacts after scoring a goal during the international friendly soccer match against Austria in Linz, Nov 14, 2012.