The 55-year-old Spaniard replaces Patrick Vieira, who has departed the MLS side after two and a half seasons to take over Ligue 1 side Nice.
“Though I have enjoyed a wonderful 11 years working alongside my colleague and close friend Pep Guardiola, it has always been my ambition to manage a team again and I really couldn’t have hoped for a better opportunity than at this football club,” Torrent said in a club release.
Torrent's head coaching experience has come in the Spanish lower divisions with Palafrugell CF, Palamos CF and Girona FC.
“Domenec is someone we know really well and have great confidence in as both a person and as a coach," NYCFC sporting director Claudio Reyna said.
"He has a very clear idea of the style of play he wants – he’s a coach who will want to play the attacking and possession style of soccer that we want to continue to build upon."
Torrent takes over NYCFC, which, as a part of City Football Group, is under the same ownership as Man City.