The 23-year-old, who was part of Italy's Under-21 team that reached the European Championship final earlier this month and played on loan for Grosseto in Italy's second tier last season, signed a four-year deal, Leverkusen said in a statement.
"We have signed a player who has a lot of room for development," said Leverkusen sports director Rudi Voller. "Giulio will give us a lot of joy in the future."
Leverkusen, who were third in the Bundesliga last season, have already reinforced their ranks with the signing of talented South Korean forward Son Heung-min from Hamburg SV last week.
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