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The Japan international will cost the French side an initial £12.9m with a further £2.5m in add-ons.
Minamino joined Liverpool for a cut-price £7.25m in January 2020 after featuring against them for Red Bull Salzburg in the Champions League but was always a fringe player and made just five starts in 30 Premier League appearances.
He was more of a cup specialist, playing a key role in last season’s Carabao and FA Cup victories, scoring seven goals in nine matches.
“It’s a great joy for me to join AS Monaco,” the player told asmonaco.com.
“I am happy to be part of the club’s project, which has just finished on the podium (third) twice in a row and is one of the most recognized in an exciting championship.
“I can’t wait to discover my new environment and do everything possible to help the team.”