The 20-year-old Argentinian midfielder moves to the Etihad Stadium on a five-and-half year deal.
Perrone made his debut for Velez in March 2022 and featured in 33 games in total, scoring three times with two assists.
He also helped the Buenos Aires Club to the semi-finals of the Copa Libertadores but missed both legs of the last-four defeat to Flamengo.
Perrone played for Argentina U-16s and is part of the national team squad competing at the U-20 South American Championship in Colombia.
Following in the footsteps of 2022 World Cup winner Julian Alvarez who moved to City last year, Perrone becomes the latest in a long line of Argentinians to join the Club.