The midfielder, 31, had a medical with Milan on Saturday as his move, reportedly worth an initial €17million, nears completion.
Milan have announced a deal for Juventus defender Leonardo Bonucci, pending the successful completion of his medical, with the deals for him and Biglia set to take the club's tally of signings for the transfer window to 10.
"I will be honest - I didn't expect this welcome," Biglia said to Sky Italia. "I am very happy."
Here's a first glimpse of Lucas Biglia in Milan— AC Milan (@acmilan) July 15, 2017
Le prime immagini di Lucas Biglia a Milano pic.twitter.com/VgSwDFURA8
Milan posted footage of Biglia's warm reception at the airport along with shots of his medical.