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.
“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 strengthened considerably this summer under Chinese owner Yonghong Li’s Rossoneri Sport Investment Lux group with Leonardo Bonucci’s €42 million move from Italian champions Juventus the headline signing so far
Vincenzo Montella has significantly overhauled his squad this summer and Biglia becomes the 10th new arrival of the transfer window at San Siro.
Milan have also signed Andre Silva for £35million from Porto, Andrea Conti from Atalanta for £21million and Turkish set piece specialist Hakan Calhanoglu from Bayer Leverkusen for £18million.
Their other deals include Mateo Musacchio arriving from Villarreal, Ricardo Rodriguez from Wolfsburg, Franck Kessie from Atalanta and the loan signing of Sunderland striker Fabio Borini.
The purchase of Gianluigi Donnarumma’s elder brother and fellow goalkeeper Antonio from Asteras Tripolis rounds off a busy window so far for Milan.