The 23-year-old Argentine has yet to make a league appearance for City since joining in 2014 from Racing Club, having done time on loan at a number of clubs including Valencia, Middlesbrough and AEK Athens.
He moved to Rayo Vallecano on a season-long loan last November but, after making nine appearances for the Spanish second division side, he has now moved to Italy and links up with his brother Franco at the Serie B leaders.
A Verona statement read: "Hellas Verona announces the loan signing of Bruno Zuculini from Manchester City. The midfielder has completed his medical and has already trained with the club, thanks to the willingness of Manchester City and Rayo Vallecano."
Zuculini has won eight caps for Argentina's Under-20 team, scoring two goals.