Vieira retired at Manchester City in 2011 and began his coaching career at City's youth team before joining NY and guiding them to successive play-off appearances.
Announcing Vieira's departure on their official website, New York City were quick to thank the former World Cup and Premier League victor for his endeavours.
The news that he would leave to take over at Ligue 1 side Nice was strangely announced on Manchester City's website, before being taken down.
He was briefly, if remotely, linked with the Arsenal job when Arsene Wenger announced his departure.
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Vieira will replace Lucien Favre at Nice, who finished eighth in the French league last season. "We know that leaving the Club has been a hard decision for him but we understand his choice to return to Europe where he spent his whole playing career".
Vieira, 41, will be joined in Nice by his assistant Christian Lattanzio and members of the NY backroom staff including performance coach Kristian Wilson and physical performance coach Matt Cook. "We have the most talented and balanced roster of players since the club was formed". His contract runs until the end of the 2020 season.
"I really couldn't have hoped for a better opportunity than at this football club", said Torrent, who has been with Guardiola the past 11 years.
Edelman was pleased to move so quickly to replace Vieira.
Torrent was born in Girona and played as a midfielder at provincial sides UE Olot and AD Guixols before moving into coaching at Palafrugell CF, Palamos CF and Girona FC. "I know Domenec can't wait to get started".
Vieira played 107 times for France and was part of the squads that won the World Cup and Euro 2000.