The Brazilian midfielder is the latest player to leave during the huge summer upheaval at Eastlands.
Elano was a revelation under Sven Goran Eriksson when he joined for £8m from Shakhtar Donetsk two years ago.
Turkish delight: Elano has ended his two-year stint with Manchester City
But he found chances limited under Mark Hughes last season, with the City boss growing tired of his questionable attitude.
The Brazil international will now hope to resurrect his career at the Turkish giants ahead of next summer's World Cup finals. He has signed a four-year deal with Galatasaray.