Rangers midfielder Joey Barton, the former England international, travelled in the opposition direction to join the French club on a season-long loan deal.
Defender Mbia, 26, who can also play in midfield, is QPR's 12th signing since the end of last season. He has agreed a two-year deal.
"Stephane is a very good player and can play in a number of positions," Rangers manager Mark Hughes told the club's website.
"He is very adept as a defensive midfielder but he has been regularly playing at centre-back so we have got another player who can add to the flexibility of the squad.
"He is a big, strong guy with a strong mentality. He wants to win and is the type of player I want at the club."
"It was an easy decision because this is an important move for my career," he explained. "It has always been a dream of mine to play in the Premier League which I believe is the best league in the world.
"The ambitions of the club and what the board of directors and the manager want to achieve here excites me greatly."
