In a statement published on the club's official website, AC Milan thanked former head coach Cristian Brocchi for his services since taking over from Sinisa Mihajlovic in April in an interim role.
Milan owner Silvio Berlusconi reportedly OK'd the deal from the hospital as he recovers from heart surgery. The Chinese consortium that's negotiating a potential takeover of the club would have also given the green light.
The Rossoneri first had to reach a settlement with Montella's club, Sampdoria, about rescinding his contract.
But those discussions were straightforward. Milan paid a relatively nominal €500,000 compensatory fee to Sampdoria to sign Montella, according to Gazzetta dello Sport's Carlo Laudisa.
Milan CEO Adriano Galliani came close to recruiting Montella two years ago when he was in charge of Fiorentina. He has now succeeded.
Montella is Milan's sixth manager in less than three years.