The Argentina international has long been linked with a move to San Siro and reports emerged on Friday to suggest a deal had at last been agreed between the clubs.
Enzo Montepaone later confirmed the 31-year-old is due in Milan on Friday to finalise the terms of a deal that will reportedly cost the Rossoneri €17 million.
"Biglia is so happy with this move," he told MilanNews.it. "He'll arrive in Milan tomorrow [Friday] and he can't wait to get started."
Biglia would become Milan's ninth signing of a hectic transfer window to date. Andre Silva, Andrea Conti, Hakan Calhanoglu, Ricardo Rodriguez, Mateo Musacchio, Franck Kessie, Antonio Donnarumma and Fabio Borini have already moved to San Siro.
However, the future of forward Suso appears to be in doubt after he was left out of the squad for the International Champions Cup in China.
The 23-year-old has been linked with a possible €22m move to Tottenham, despite having insisted this month that he had no plans to leave.
Alessio Romagnoli, Manuel Locatelli, Davide Calabria and Gianluca Lapadula are also missing from the 26-man squad.