Bonucci, capped 80 times by Italy, spent seven years at Juventus, where he won six Serie A titles and reached two Champions League finals.
On Thursday afternoon, Juve tweeted a short video of former skipper Bonucci with the caption "he is here in Turin".
Milan's Instagram account, meanwhile, posted a video of Higuain in the club's colours with the caption "Higuain, ready to start".
The Rossoneri will reportedly pay an initial £16m as part of a season-long loan deal for the Argentine, with the option of making the move permanent for an additional £32m at the end of the season.
Milan have recently been taken over by American hedge fund Elliot Management after the previous Chinese owners failed to repay a loan owed to the fund.