Bonucci, who won six straight Serie A titles with Juventus, became Milan's 10th new signing of the summer.
Inter Milan winger Ivan Perisic will play in a preseason friendly against Schalke on Friday as uncertainty continues to surround his future.
Aleksandar Kolarov is close to joining Roma after telling Pep Guardiola that he wants to leave Manchester City.
The technical director of Inter Milan's owners Suning Sports, Walter Sabatini, says that no suitable offer has yet been received for Ivan Perisic.
Roma have confirmed the arrival of striker Gregoire Defrel from Sassuolo on an initial loan deal which could become permanent and reach €23 million.
AC Milan have completed the signing of Italy defender Leonardo Bonucci from Juventus for €42 million.