The newly promoted club have prised one of the most exciting young forwards in France away from their Ligue 1 rivals
The teenage striker, who came through the youth team ranks at the Gerland, has signed a three-year contract with les Rouge et Blanc.
"We are very happy that Anthony is joining us," Monaco technical director Riccardo Pecini told the club's official website. "He is the big hope of his generation and he will continue to grow at a very high level."
The 17-year-old forward, who has been capped by France at Under-18 level, only made his Ligue 1 debut earlier this year.