The 21-year-old joined the Premier League champions for their pre-season tour of the United States and scored in the 4-1 victory over Sporting Kansas City on July 24.
City have not disclosed a fee or length of contract for the highly rated youngster, who joins fellow Argentinians Sergio Aguero, Martin Demichelis and Pablo Zabaleta at the Etihad Stadium.
"I'm very excited about the future," Zuculini told the club's official website.
"I am looking forward to the experiences which this move will bring and to improving myself as a player.
"I'm also very proud to be the fourth Argentine to sign for City. The Club is very popular in Argentina because of Sergio Aguero, Pablo Zabaleta and Martin Demichelis."
Zuculini has represented Argentina at under-20 level and made 92 appearances for Racing Club, scoring 10 goals.
He is available for selection in City's Community Shield clash with Arsenal on Sunday.
