All three players underwent medical examinations on Thursday morning.
Higuain is set to finalise a one-year loan switch worth an initial €18 million (£16m/$21m), with the Rossoneri able to make the deal permanent with a €36m (£32m/$42m) payment at the end of the season.
With Bonucci having spent only a season with Milan, Juve boss Allegri is happy to have a defensive stalwart return to Turin.
“Leonardo is back after one year. He is an important player,” the head coach told Sky Sport Italy.
“In six months he has not changed at all.
“Caldara is younger and along with [Alessio] Romagnoli and [Daniele] Rugani is part of the best defending trio in Italy. I am sorry but the circumstances forced us to let him go.
“As for Higuain, I thank him for these two seasons during which he gave his best. Milan have signed a great striker, for sure.”
Higuain scored 40 Serie A goals for Juve after joining from Napoli in 2016.
Caldara, who officially signed from Atalanta in January 2017, failed to make a competitive appearance having remained on loan at his boyhood club last term.