The 16-year-old Italy youth international is one of the most highly-rated youngsters in European football following a series of impressive displays for the Griffins.
Pellegri is the joint-youngest player to have debuted in the Italian top flight, taking to the field against Torino in December 2016 aged 15 years and 280 days.
Speaking to Monaco's official website, Pellegri said: "I am very pleased to join AS Monaco.
"I was quickly convinced by the project which helps young players like me to be able to grow and flourish in the future.
"I'll work hard to become a major player in the club."
Pellegri had made seven appearances for Genoa this season, scoring two goals.