He left City after a shock FA Cup final loss to Wigan Athletic and a poor defense of their title, as well as another failure to progress out of the Champions League group stage.
The stylish 49-year-old was appointed Galatasaray coach following the dismissal of Fatih Terim, taking charge only two days before a Champions League match with Juventus.
Having recently said he wanted to remain in Turkey, he has left after what appears to be a difference of opinion about the direction of the team.
"As a coach I understand the demands of the club. However, when I accepted the coaching post, Gala’s aims were different," Mancini told Gazzetta dello Sport.
"In the past eight months, despite enduring a challenging start, I have done my job pushed by passion and by hunger which has resulted in the team qualifying for the Champions League, lifting the Turkish Cup and finishing second in the league.
"It’s with sadness that I leave Istanbul and the club’s fantastic supporters."
Galatasaray were runners-up in the league to bitter city rivals Fenerbahce while their victory in the Turkish Cup final was over Eskisehirspor.
Mancini's side progressed to the Champions League round of 16 at the expense of Juventus, but were then knocked out by Chelsea.
"Our relationship with the coach Roberto Mancini and his contract of employment, which was signed on 1 October, 2013, has been terminated by mutual agreement," the club said in a statement. "We wholeheartedly thank him for his success and achievements and wish him happiness in his next mission."
Former Italy forward Mancini has also coached Fiorentina, Lazio and Inter Milan, winning four Italian Cups and three Serie A titles in total, with recent speculation linking him with a return to Italy.
(Reporting by Josh Reich; Editing by John O'Brien/Alan Baldwin)
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