The 23-year-old has signed a five-year deal at the Stade Louis II and is reported to have cost Monaco €11million.
Jean Lucas spent two seasons with Lyon but made just 25 appearances for Les Gones in all competitions and was loaned to Brest for the second half of last season.
He has 67 top-flight games under his belt in Brazil and France, having also previously played for Flamengo and Santos, scoring three goals and assisting five more across those matches.
Monaco announced the signing on its official website on Monday and Jean Lucas said: "I am proud to join AS Monaco, one of the biggest clubs in Ligue 1.
"The club had a great season and will be fighting for a place in the Champions League group stage. I am happy to have the opportunity to contribute to this sort of growth."
Monaco begins its 2021-2022 campaign on Wednesday (AEST) with the first leg of its Champions League third-qualifying round tie against Sparta Prague.