The 19-year-old, who was already on loan in Ligue 1 at Lille last season, cost Monaco around 10 million euros ($11.25 million) according to various French media.
"AS Monaco are an excellent team at which to progress, it's a good challenge for me," said Lopes, who was born in Brazil, on the club's website.
Monaco coach Leonardo Jardim said his compatriot would not be ready for first team action immediately and may go out on loan.
"He needs to know how we work and our methodology here at Monaco -- that will take five or six months.
"After that, we'll see in January if we send him on loan."
Lopes scored three goals in 23 Ligue 1 matches for Lille last season.