The 59-year-old has been out of job since leaving England following the 2006 World Cup but former Thailand Prime Minister Thaksin Shinawatra, who is close to gaining full control of the club, gave him a new challenge.
Eriksson, who has signed a three-year deal, spoke of his excitement at managing City in a high-profile league like the Premiership.
"Manchester City is a big, big football club, there's a new owner with more money to buy better players, it's the Premier League but my main reason was because this is a very big football club."
"It's always good to take on a job that's a challenge, and this is a great challenge for me. I'm very excited, I'm looking forward to it, I'm sure that the players and the staff are, and I know that the fans will be very excited as well."
The Swede manager will be hoping to improve on City's 14-place finish in the Premiership last season.