The deal includes an option for Sunderland to make the transfer permanent at the end of the season.
“I’m very happy to be a Sunderland player. I had a very good feeling training with the team,” M’Vila, 25, told the club website.
“Every player welcomed me and the feeling was very good with them so I’m excited for the start of the season. I’ve also wanted to play in the Barclays Premier League for a long time so I’m very happy to be here.”
M’Vila, a holding midfielder, began his career with Rennes and broke into the France team under Laurent Blanc in 2010.
He won 22 caps but has not represented his country since 2012, having been banned from playing international matches for 19 months following an unauthorised night out while on duty with France’s under-21s.
M’Vila has a reputation as a troublemaker and his career has been on the slide since he left Rennes for Kazan in January 2013, with a loan spell at Inter Milan last season yielding just eight league appearances.
He is Sunderland manager Dick Advocaat’s fifth signing of the close season, after Jeremain Lens, Younes Kaboul, Sebastian Coates and Adam Matthews, and could make his debut at Leicester City on Saturday. – Agence France-Presse