The 21-year-old midfielder has featured in all of City's pre-season fixtures this summer and found the net in the 4-1 win over Sporting Kansas City.
City have also confirmed that Zuculini is in contention for selection for Sunday's Community Shield match against Arsenal.
“I’m very excited about the future,” the youngster 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, an Argentina Under-20s international, is City's fifth arrival this summer after Bacary Sagna, Fernando, Willy Caballero and Frank Lampard.