Bonucci, 30, is joining Milan on a five-year deal after seven seasons in Turin, where he won six successive Serie A titles with Juventus and played in two Champions League finals.
"Seven seasons have gone by. Seven seasons of victories, of dreams achieved, of maturity gained thanks to this exceptional bond with Juve," Bonucci wrote in the Gazzetta dello Sport daily.
"I truly always gave everything until the end. I have received, given and learned. And what I see today, looking back, is a splendid story worthy of ending in full respect and affection, without questioning anything I went through with the club, the captain, my colleagues and the fans," he added.
Bonucci's arrival in Milan comes after heavy investment from the seven-time Europeans champions following the sale of the club by former Italian Prime Minister Silvio Berlusconi to a Chinese consortium in April.
Milan came sixth in Serie A last season, the club's highest finish since the 2012-13 campaign, and are plotting a return to the Champions League after a four-year exile.