The 23-year has shone at the recent European championships in Italy's youth team which saw them reach the final before succumbing to Spain.
Donati joined Inter Milan in 2009 but since joining the San Siro side he has been largely on the outer with loan spells at Lecce, Padova and this season Grosseto.
"I am happy that the deal has been completed," Donati told the club's official website.
"Bayer are a big team in Germany and also have a big reputation in Italy. I am really looking forward to the Bundesliga and it will be a huge challenge to play in the Champions League with Leverkusen.
"I will give my all to help B04 achieve their goals."
The right back is most likely a replacement for Dani Carvajel who re-signed with Real Madrid due to a buy-back clause is the defender's contract at Leverkusen.
Donati made 27 appearances in Serie B last season.