Monaco announced the signing of the 29-year-old yesterday on a three-year deal for an undisclosed fee.
The winger made 37 appearances for the Baggies, scoring six goals, and helped Belgium finish in third place in the World Cup this summer.
Chadli told Monaco's official website: "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."
The Belgium international could make his debut when Monaco host Marseille in Ligue 1 on Sunday.