The 35-year-old Frenchman, who was released by City at the end of last season, has accepted the position of football development executive and will help in the development of young players among other responsibilities.
Vieira said: "This role is a fantastic new challenge for me and I am very grateful to Manchester City for offering me this opportunity."
He added: "I have a lot to learn about the non-playing areas of the business but there are many very experienced people here for me to learn from and I am confident that I can make a significant contribution to the club's ongoing success."
Vieira was City boss Roberto Mancini's first signing when he left Inter Milan to return to the Barclays Premier League in January 2010.
He was not a regular starter but made 47 appearances in total, scoring six goals, with his final run-out in a City shirt coming as a late substitute in the FA Cup final victory over Stoke in May.
As well as working in the youth set-up, Vieira will also help to deliver the club's social responsibility programme and get involved on the commercial side.
The Frenchman added: "I am particularly pleased to be given the opportunity to work with the club's community scheme.
"Manchester City has a great reputation for its commitment to its community and charity partners and I believe I can help to take that message to an even greater audience.
"Everyone at Manchester City - the fans, the staff and the players - have made me and my family feel very welcome here over the past two years and I am very happy to have been given the chance to stay and develop my career away from the pitch."
Source: PA
Source: PA