West Brom, who were relegated from the Premier League last season, said the deal was concluded after the Ligue 1 side made an improved offer for Chadli late on Wednesday.
British media said Monaco paid a fee of 10 million pounds ($13.01 million) for the 29-year-old attacking midfielder.
"I am very happy to join AS Monaco, a great French club that participates in the Champions League," Chadli was quoted as saying on the French principality club's official website.
"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."
Monaco, who finished second in Ligue 1 last season, were on Thursday drawn to play Atletico Madrid, Borussia Dortmund and Club Bruges in Champions League Group A.
"We are delighted to welcome Nacer Chadli, an offensive midfielder who has demonstrated his quality. His experience at the highest level and his technical profile will be additional assets for the team," said Monaco CEO Vadim Vasilyev.
Chadli captured the headlines at this year's World Cup in Russia when he scored a stoppage-time goal for Belgium in a 3-2 win over Japan in the last 16 and they went on to finish third.
He started out at Dutch second division club AGOVV Apeldoorn before joining FC Twente where he scored 25 goals in 84 league games and earned a move to Tottenham Hotspur in 2013.
Chadli went to West Brom three years later and made 32 appearances in his first campaign but was then restricted by injury and featured in just five during the 2017/18 season.
($1 = 0.7687 pounds)
(Writing by Ken Ferris; Editing by Greg Stutchbury)
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