Vieira led New York City to two consecutive playoff appearances and leaves with the team in second place in the Eastern Conference.
He then moved into coaching taking charge of the under-19 and under-21 Manchester City teams before coaching NY, which shares its owner with City.
But as a coach he has only been part of the City Football Group - which owns both the Manchester and NY clubs.
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Assistant coach Christian Lattanzio, performance coach Kristian Wilson and physical performance coach Matt Cook have also left NY to join Vieira at Nice.
A few weeks ago, NYCFC launched a new training ground with a tour for media members that stopped in front of one door that remained closed, the room housing the database of players and scouting files, that CFG staff referred to, only half tongue-in-cheek, as "the Crown Jewels".
"Patrick has been a fantastic role model at NYCFC and a true leader on and off the field".
Vieira retired as a player in 2011 and moved into coaching taking charge of the under-19 and under-21 Manchester City teams before coaching NY, which shares its owner with City. His contract runs until the end of the 2020 season. "I'm very happy to be here".
While NYCFC don't play until June 24 against Toronto FC, the move has been brewing for multiple weeks, with Vieira's exit becoming increasingly more likely. "I know Domenec can't wait to get started".
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. He also won 107 caps for France, winning the World Cup in 1998 and European Championship two years later.