The centre-back was shown arriving at Milan's headquarters in a video on the club's Twitter feed.
The San Siro giants are still trying to rediscover the form that saw them dominate Italian football for many years and they only managed a sixth-place finish last season to qualify for the Europa League. "Our objective has to be getting into the Champions League and that is a very exciting challenge, especially with all the new signings".
GETTY Leonardo Bonucci has signed for AC Milan
Milan will reportedly pay a 40 million euro ($45 million) transfer fee to Juventus and sign Bonucci to a five-year contract worth up to 10 million euros ($11 million) per season, including bonuses.
Portuguese forward Andre Silva has joined from Porto, with Turkey midfielder Hakan Calhanoglu moving from Bayer Leverkusen and Swiss full-back Ricardo Rodriguez arriving from Wolfsburg.
"Claps of thunder" in the title race suggested Gazetta dello Sport, while Corriere della Sera believes "Milan can win the Scudetto with Bonucci".