Milan completed a major coup with the signing of Juventus defensive lynchpin Leonardo Bonucci for €42 million ($62.6 million) on Friday and Biglia becomes the 10th new arrival of the transfer window at San Siro.
The Argentina international has long been a target for Milan and the Rossoneri have paid a reported €17 million ($24.93 million) to bring him to the club, with Biglia signing a three-year contract.
Vincenzo Montella has significantly overhauled his squad after signing a new contract in May and Biglia is the latest fresh face through the door ahead of the new Serie A season.
Andrea Conti, Andre Silva, Hakan Calhanoglu, Mateo Musacchio, Ricardo Rodriguez, Franck Kessie, Antonio Donnarumma and Fabio Borini have all completed moves to Milan, with the club's heavy spending set to continue.
Milan also tied down their highly-rated teenage goalkeeper Gianluigi Donnarumma to a long-term contract, the Italy international performing a U-turn after his agent Mino Raiola indicated he would not agree an extended deal, before his older brother Antonio returned to the club.
Montella is reportedly keen to sign another striker to compete for places with Portugal international Silva, with Milan having been linked with Torino's Andrea Belotti and Pierre-Emerick Aubameyang of Borussia Dortmund.