The Belgian winger, who played a part for his country at the World Cup, will leave for a £10 million fee.
The 29-year-old signed a three year contract with the Ligue 1 side.
He will participate in the UEFA Champions League with his new club.
Chadli told asmonaco.com: "I am very happy to join AS Monaco, a great French club that participates in the Champions League.
"The results of the last seasons prove the quality of the project and the ambition of the club.
"I will do everything to help AS Monaco achieve great things and achieve its goals."