The midfielder, who becomes the tenth first team summer addition, has put pen to paper on a four-year-deal.
Saïss made 35 appearances for Angers in 2015/16, helping the club to a ninth-place Ligue 1 finish.
Prior to his time with Angers, the 26-year-old enjoyed spells with Le Havre, Clermont and Olympique de Valence.
The midfielder has also featured at international level for Morocco, making five appearances during his career.
Speaking after joining the Club, Saïss said: "I am very happy to be here. Wolves is a good club for me.
"It has a good project to get to the Premier League.
"The stadium, the fans and the training facilities are fantastic and I'm really happy to come here.
"I hope to play in many matches and help take the club to the Premier League as soon as possible."