"I can't wait to meet my new team mates, to learn more about the city, the (Tatarstan) region and the (Russian) league," the 22-year-old told Rubin's website.
"I'm thankful to Rennes, where I had spent the last nine seasons and where I've grown to become a professional player.
"I'm also thankful to Rubin for giving me the opportunity to show my best in the new club. This is a new challenge in my career."
Kazan outbid English Premier League clubs Queens Park Rangers and their London rivals Fulham by shelling out 12 million euros and offering M'Vila a reported annual salary of more than four million euros.
The big paycheck apparently has helped persuade the talented Frenchman to make his move to Russia. Last August, he declined to join Russian champions Zenit St Petersburg after reportedly receiving death threats from some of the Zenit fans.
M'Vila has also courted controversy. Last November, he was banned from all national teams until June 2014 after an unauthorised night out while on Under-21 duty.
The Russian league season resumes in mid-March after a three-month winter break while Rubin also face holders Atletico Madrid in next month's Europa League last 32 tie.