Eriksson visited City's training ground this week as the squad returned for pre-season training, and the 59-year-old Swede today signed a three-year contract with the Blues.
"I am absolutely delighted and honoured to have been asked to be Manchester City's manager," he told the City website.
"This is an exciting challenge and I have already started making preparations for the new season. I want to deliver a team that our fantastic fans can be proud of."
Chief Executive Alistair Mackintosh added: "I'm delighted that Sven-Goran Eriksson has agreed to join the club as we move into an exciting new era.
"Sven's vast experience of managing top clubs to success around Europe is one of the qualities that attracted us to him. He also knows the English Premier League inside out from his time as national team manager."