Bonucci, capped 80 times by Italy, spent seven years at Juventus, where he won six Serie A titles and reached two Champions League finals, before leaving for San Siro last summer.
Milan will reportedly pay an initial £16m as part of a season-long loan deal for Higuain, with the option of making the move permanent for an additional £32m at the end of the season.
Caldara, meanwhile, spent just one month at Juventus following his move from Atalanta and has been used as a makeweight in the deal to bring back Bonucci.
"After spending seven wonderful years in black and white, Leonardo Bonucci has returned to the club following a season at AC Milan," Juve said in a statement. "Both Juventus and Bonucci are ready to start winning things again together."
Milan's acquisitions, meanwhile, were described as follows: "Gonzalo and Mattia are two important pieces of the new era of the club."
Juve won the Serie A championship last term, while Milan finished sixth in the standings.