The former French international succeeds Lucien Favre, who left to manage Borussia Dortmund.
Vieira, 41, has been in charge of the MLS franchise since 2016, having led Manchester City reserves following his retirement from playing.
The former Arsenal man said his goodbyes in a statement that was then removed from City’s website.
He said: “I would like to thank City Football Group and New York City FC for the opportunity to have coached this tremendous football club.
"Leaving New York is an incredibly difficult decision for me and for my family and one that has not been taken lightly.”
Vieira was on the Gunners list to replace Arsene Wenger, but was unhappy with his former club’s approach and felt it was a token gesture.
Arsenal opted to hire former Paris Saint-Germain boss Unai Emery as head coach.
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But Vieira, who began his career at nearby Cannes has seen a return to Europe as the next step in his managerial journey.
Nice finished third in Ligue 1 in 2017, but were unable to repeat their success last term finishing eighth.
Confirming the news on their official website, Nice said: "Arriving in Nice in the middle of the morning, Patrick Vieira has officially signed his contract.
"The former French national team’s captain, until now coach of New York City FC, will follow in Lucien Favre’s footsteps.
"He will return to L1 as coach of the Aiglons, almost 23 years after leaving it as a player."
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