Reports in Italy suggest that while Calhanoglu will cost Milan an initial €20m, it is a deal that could rise in value to €24m once add-ons are taken into account.
The Turkey international has not played since January due to a FIFA ban relating to contract dispute with Trabzonspor, whom he is said to have agreed to join before pulling out in 2011, being upheld by the Court of Arbitration for Sport.
The 23-year-old waived his wages for the duration of his four-month suspension and reportedly opted against an appeal in order to be available for a transfer in the close-season.
Calhanoglu told Leverkusen s website: The three years at Bayer were very emotional.
I would like to thank the club, the staff and above all the fans. The support was sensational, especially during my four-month suspension. Now I want to open a new chapter in my career.