The former Arsenal and France international midfielder has been appointed as the new manager of the Major League Soccer outfit.
Lescott, who joined Villa from Premier League rivals West Bromwich Albion in the summer transfer window, played with Vieira at Manchester City.
The 33-year-old England international defender has taken to Twitter to wish Vieira the best of luck at New York City.
New York City finished eighth in the MLS Eastern Conference table during the 2015 campaign and 17th in the overall standings.
The Yankee Stadium-based outfit have some well-known players on their books, such as former Barcelona star David Villa, Chelsea legend Frank Lampard, AC Milan and Juventus great Andrea Pirlo.
Vieira will be looking to guide New York City FC to the MLS playoffs at least during the 2016 campaign.