The 26-year-old has penned a four-year deal at Molineux and becomes Wolves' 11th signing of the summer - and the 10th since Fosun bought the club last month.
The fee is undisclosed but reports in France suggest it is around the £3million mark.
Moroccan international Saiss was player of the year for Angers in Ligue 1 last season.
Saiss - who can also play at centre half - said today: "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."