Minamo has left Liverpool for ASM in a €17m deal.
He scored 10 goals in 24 appearances last season and was the top scorer for the Reds in both the FA Cup and League Cup, which Liverpool won. However, he only made one Premier League start, although he did score in that game, a 2-1 victory at Southampton.
"It is a great joy for me to join AS Monaco," he told the club's official website.
“I am happy to be part of this very exciting project, at a club with a great tradition and among the most recognised in Ligue 1. I am looking forward to discovering my new environment and doing everything I can to help the team."