The Turkish side confirmed the move had been finalised on Friday, a deal that will cost them a transfer fee of €5.25 million, which could rise by a further €900,000 in bonuses.
Gala also revealed Fernando has signed a three-year deal and will earn an annual salary of €3.3m.
The 30-year-old spent three seasons with City, who he joined from Porto in 2014, but only started five Premier League matches in 2016-17, Pep Guardiola's first campaign in charge.
City had left Fernando, who leaves with the 2016 League Cup as his only major honour, out of their pre-season tour of the United States prior to Gala confirming talks over a move on Thursday.
The Brazilian was grateful for his three years in England, telling the club's website: "It has been a pleasure to play for Manchester City.
"The Club has looked after me incredibly well throughout my time here and I have enjoyed the challenge of playing for a top team in probably the world's toughest league.
"The League Cup success of 2016 was a highlight for me and something I will never forget."
Director of football Txiki Begiristain thanked him for his service, saying: "Fernando has been an excellent servant for City. "He is a dedicated professional and a player who has made a significant contribution throughout his time here.
"I am sure he will continue to prove his quality for years to come."
Guardiola has now sold or released eight players from last season's squad in his transfer-window clearout, Fernando following Kelechi Iheanacho, Nolito, Aleksandar Kolarov, Willy Caballero, Jesus Navas, Gael Clichy and Pablo Zabaleta out of the exit door.