The Baggies revealed that the deal was completed on Thursday evening after an improved offer from the Ligue 1 side was accepted late on Wednesday.
Chadli joined Albion in the summer of 2016 from Tottenham Hotspur and made 32 appearances in his first campaign for the West Midlands club.
However, the 29-year-old barely featured last season as the club were relegated from the Premier League.
Chadli went on to impress for Belgium at the World Cup, becoming the first West Brom player to feature in a semi-final, as the Red Devils finished third in Russia.
The versatile player scored six goals in 36 league appearances for the Baggies.