The Brazilian attacking midfielder has signed a five-year deal with Leonardo Jardim’s side.
Boschilia, who has been involved with Sao Paulo’s first-team squad for around 18 months, was a key part of the Brazil Under-20 side who finished as runners-up in the World Cup earlier this summer.
"I am very proud to commit myself to AS Monaco and to have the opportunity to work at a big club,” the 19-year-old told his new club’s official website after signing.
“I will do everything to help the team and put forward my skills in service of the collective.”
"We are very proud to welcome him,” he said. “Gabriel is a young Brazilian prospect who shone during the Under-20 World Cup and we have regularly followed him.
“He is only 19 and we believe in him a lot. We are convinced being at AS Monaco will enable him to grow and he will demonstrate his full potential playing alongside our other players."
The signing came as Monaco tied star Portuguese playmaker Bernardo Silva to a new contract that will also keep him in the principality until 2020.