Celtic have signed defender Dedryck Boyata from Manchester City on a four-year contract.
M'Vila arrived in Milan last week and underwent a medical but waited until Tuesday morning to finally train with the Nerazzurri outfit.
Inter posted a photograph of M'Vila on the club's website, www.inter.it, with a statement that read: "M'Vila joins his new team-mates on the pitch for the first time in Inter's Pinzolo training session."
As part of the agreement, Inter have an option to make the switch permanent next summer.
M'Vila joined Rubin Kazan from Rennes in January 2013 in a reported £9.6million transfer deal.
The 24-year-old has three years left on his contract with the Russian outfit.
Since June 30, M'Vila can return to represent France after serving a 16-month ban over an unauthorised night out when on Under-21 international duty.