Financial details were not disclosed but Italian media reported that the transfer fee for the 23-year-old was around 23 million euros ($27 million).
A product of the Empoli academy, Ricci made the switch to Torino in 2022 and went on to make 113 appearances for the club. He has won 10 caps for Italy since his debut in 2022.
Ricci's arrival will boost Milan's midfield options following Tijjani Reijnders' move to Manchester City.