The 21-year-old made 30 appearances in two seasons with Verona after joining from Manchester United in 2014.
"We have managed to sign him despite the fact he was being chased by a number of top sides and that is a great sign," boss Roberto Di Matteo said.
"He's a young man but has plenty of experience and I'm sure he'll prove to be an excellent signing for the club."
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Aston Villa have signed goalkeeper Pierluigi Gollini from Italian side Hellas Verona on a four-year deal.