The 19-year-old has signed a five-year contract, which will keep him at Juventus until the summer of 2017.
“It’s a dream come true,” Leali told the club’s official website.
“Joining such a prestigious club at my age is extremely gratifying and a great motivation to keep developing further.
“Being part of the same club as a champion like Gigi Buffon is hugely satisfying, but it also makes me realise how much I’ll have to work for the opportunity to repay the trust placed in me.”