Duff left Fulham at the end of the season and his deal with City comes in under the salary cap, leaving them free to make another international marquee signing.
The 35-year-old will join a squad including former Barcelona star David Villa, who is linking up with Melbourne before he joins New York City FC for their inaugural MLS season in 2015 - both clubs are majority owned by Manchester City.
Duff won the Premier League title twice with Chelsea and earned 100 caps for the Republic of Ireland - he also played for Newcastle and Blackburn in the Premier League.
Coach John van't Schip said: "We're excited to have a player of Damien's quality and experience for this season. We believe he can offer international standard quality on the pitch and will also be a great professional example for our younger players.
"His career speaks for itself. He has achieved almost everything at club level and has been a great player at an international level too. He comes to us straight from the English Premier League with Fulham, so he has been playing at the highest level against top teams and top players.
"When we met with Damien, he was excited about the opportunity here and keen to work with us to help make this project a success."