The 27-year-old put pen to paper on a four-year contract in France after spending two years with the Premier League club.
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Minamino arrived at Anfield in January 2020 after signing for £7.25 million from FC Salzburg but failed to hold down a regular place in Jurgen Klopp's first team.
"It is a great joy for me to join AS Monaco," Minamino told the club's official website. "I am very happy to be part of this very exciting project, at a club with a great tradition and among the most recognized in Ligue 1.
"I'm looking forward to discovering my new environment and doing everything I can to help the team."
Last season, he started just once in the Premier League, scoring in the penultimate game of the season against Southampton. The forward scored 10 goals in 22 appearances across all competitions last term.
The arrival of winger Luis Diaz in January further limited Minamino's first-team opportunities, with the Colombian making a hugely impressive start to life on Merseyside. Already this summer, Uruguayan striker Darwin Nunez has been signed in a club-record deal and forward Fabio Carvalho has joined from Fulham to further boost Liverpool's attacking options and compensate for the loss of Sadio Mane to Bayern Munich.
Following the news of Minamino's departure, Klopp praised the forward's contribution since joining Liverpool two years ago.
"It's hard to see Taki go, but it's a great move for him and one he thoroughly deserves," he told Liverpool's website on Tuesday. "An amazing professional; super, talented player. As a person, he is full of warmth and makes everyone feel positive. A manager's dream, to be honest.
"I'm sure there will be those who think it didn't quite work out. Those who think this are wrong. I don't accept that. His contribution far outweighs the opportunities we were able to give, in terms of starting matches.
"He made us better each and every day he was with us - not just in the games he played in but every single session in training. Perfect attitude, winner's mentality.
"His performances and his goals are the reason we have had to redecorate the Champions Wall so often. His achievements here will stand the test of time.
"I know he will be a big success at Monaco. I'm sure we will look on with a mix of celebration and envy as he progresses and flourishes there.
"He leaves with our appreciation and best wishes. Thank you, Taki."
Minamino, who spent the second half of the 2020-21 season on loan at Southampton, finished with 14 goals in 55 appearances in all competitions for Liverpool.
Monaco finished third in Ligue 1 last season to earn a place in the Champions League.