The Frenchman joined City as a player in January 2010, and after retiring from football the following year he moved into a youth development role at the Etihad Stadium.
Having achieved his Uefa 'B' coaching license in 2012, while continuing to work towards his 'A' license, Vieira will now take charge of the Elite Development Squad, which plays in the Under-21 Premier League.
"After spending two years working across a number of areas of the club and with a particular focus on the youth academy, I feel honoured and privileged to have been offered this role," he told the club's official website.
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Ferran Soriano, who replaced the controversial Garry Cook as chief executive last August, hopes the World Cup and European Championship winner will be able to transfer his knowledge to City's youngsters.
"Patrick is a world champion and it is a great honour that he has chosen Manchester City to begin his football management career," the former Barcelona director added.
"I have seen him carefully considering options and choosing to coach for the best reasons; he has a love of the game and a willingness to continue to learn and transmit his knowledge and experience to young footballers.
"Patrick’s role is of the highest long term importance for the club. The ability of the academy, the Elite Development Squad and the first team to work together using the same football concepts is key to our success and sustainability."Vieira will replace Attilio Lombardo, who City say has stepped down from the role, though the club cut at least 10 members of the coaching staff following the sacking of Roberto Mancini.
Lombardo was installed during Mancini's tenure, but the club are keen to move in a more "holistic" direction following the former Inter boss' departure.