Having left Fulham on a free transfer following their relegation from the Premier League, Duff has been recruited by City under the salary cap, meaning speculation will continue over potential high profile arrivals at the club.
John van 't Schip's team, who will be able to call on the services of David Villa before he joins New York City FC for the 2015 MLS campaign, are yet to announce their international or domestic marquee players for the 2014-15 season.
They also have one further spot for an overseas player to be paid under the cap.
Duff, who won the Premier League twice with Chelsea and earned 100 caps for the Republic of Ireland, left Fulham at the end of last season after five years at Craven Cottage.
The 35-year-old also played for Newcastle United for three years after leaving Chelsea in 2006.
"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," Van 't Schip said in a statement.
"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."