The Turkey international has signed a four-year deal at San Siro and becomes the sixth signing of what is turning into a busy summer for Vincenzo Montella's side.
He joins Mateo Mussachio, Franck Kessie, Ricardo Rodriguez, Andre Silva and Fabio Borini in moving to the Serie A giants, with the spending for the off-season now standing at around €130m.
Calhanoglu leaves Leverkusen having scored 17 goals in 79 appearances during three years representing the Bundesliga outfit, and has a reputation as an expert from set-pieces.
He has not played since February, however, after being handed a four-month ban for breaking the terms of his contract when joining Trabzonspor in 2011.
Speaking to Leverkusen's offficial website, he said: "I would like to thank the club, my colleagues and above all the fans.
"The support was sensational, even during my four-month ban."
The 23-year-old arrived in Milan on Sunday before completing a medical on Monday and finalising the terms of his move.