The France midfielder, who has been linked with a number of Premier League clubs this month, is undergoing a medical in Rome ahead of a potential switch to the Russian outfit.
The 22-year-old has been touted for a move away from the club for some time, with Premier League sides Tottenham and QPR thought to be at the front of a long list of admirers, before the Ligue 1 club made an announcement on its official website
"Stade Rennais FC, Rubin Kazan and Yann M'Vila have reached an agreement for the permanent transfer of the French international. After undergoing a medical, the Rennes midfielder will join the Russian club officially on Wednesday evening," the statement read.
Earlier, Rubin's vice president Kamil Ishakov admitted the player was close to sealing a switch, but for the ironing out of the final details of the deal.
He told Sport-Express: "M'Vila attracts many European clubs. In England, clubs such as QPR, Fulham and Arsenal have, like Rubin, made concrete proposals.
"[But] Negotiations are currently in our favor. There are still some details, including the final results of the medical visit which takes place in Rome. Once the results are published, all will be decided. It is possible that he could sign the contract tonight."