The 27-year-old officially departed Anfield at the end of June following the expiration of his contract and has signed a four-year deal with the Italian champions.
Origi scored a plethora of crucial late goals for Liverpool during his eight-year spell at the club, but he consistently struggled to become a regular starter of Jurgen Klopp's.
Origi arrived in Milan at the end of last month to complete his medical and sign his long-term contract with the Rossoneri, who have now announced the striker's signing.
The former Lille and Wolfsburg man arrives at San Siro to compete with Olivier Giroud and Zlatan Ibrahimovic in the attacking ranks, although the latter is out until 2023 after undergoing knee surgery.
Following confirmation that Origi would leave Liverpool at the end of the season, Reds manager Jurgen Klopp paid a special tribute to the Belgium international before their final game of the Premier League season against Wolverhampton Wanderers.
"I expect Div to get a special reception. One of the most important players I ever had. He was and is a pure joy to work with," Klopp told reporters.
"It's not over yet but he deserves all good thought we can generate for his future. He'll be a success. I remember so many things when I think about Div. Goals, ups and downs. A Liverpool legend."
Origi left Liverpool with 41 goals and 18 assists under his belt from 175 competitive matches, including his side's second in the 2019 Champions League final against Tottenham Hotspur.
Origi had previously scored a memorable brace against Barcelona in the semi-finals of the tournament, and he managed a respectable six goals and four assists from 18 outings in all tournaments in 2021-22.
Origi has become Milan's second official signing of the summer window after Stefano Pioli's side welcomed Alessandro Florenzi to the club from Roma on a permanent deal following his loan spell last term. body check tags ::