Mbia has signed a two-year contract and joins Rangers for an undisclosed fee.
Rangers boss Mark Hughes said: "Stephane is a very good player, and is another who can play in a number of positions.
"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.
"We have been talking about getting a centre back and he is in my mind for that role, but he is just as adept in midfield and I wouldn’t have any worries about playing him in either position."
Mbia added: "It was an easy decision because this is an important move for my career.
"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.
"I am so happy and enthusiastic about what the future holds here and can’t wait to be part of this exciting project."