The 31-year-old won four Belgian titles with Anderlecht before moving to Lazio in 2013. He scored four goals in 29 league appearances last season as Lazio finished fifth.
"AC Milan are delighted to announce the signing of Lucas Biglia from SS Lazio. The player has penned a three-year contract through to 30 June 2020," the club said on their website. (www.acmilan.com)
"The Argentinian is a quality player with a strong tactical sense. Biglia is important on and off the ball, starting the move for the team, with great vision of play and a talented set piece taker."
Milan have finished outside the top five for the last four seasons.