The Italian club has the option to make the switch permanent when it expires next summer.
The 24-year-old Frenchman arrived in Milan last week for a medical before completing his temporary move on Tuesday morning.
M'Vila has three years remaining on his contract with Rubin after joining the club from Rennes in January 2013.
He has scored one goal in 22 appearances for the France national team.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | FC KrasnodarKrasnodar | 10 | 7 | 3 | 0 | 18 | 5 | 13 | 24 |
| 2 | Lokomotiv MoscowLokomotiv | 10 | 8 | 0 | 2 | 25 | 14 | 11 | 24 |
| 3 | Zenit St PetersburgZenit | 10 | 7 | 2 | 1 | 22 | 4 | 18 | 23 |
| 4 | Dynamo Moscow | 10 | 6 | 2 | 2 | 18 | 10 | 8 | 20 |
| 5 | CSKA MoscowCSKA | 10 | 5 | 2 | 3 | 19 | 6 | 13 | 17 |
| 6 | Spartak Moscow | 10 | 4 | 4 | 2 | 14 | 9 | 5 | 16 |
| 7 | Rubin Kazan | 10 | 3 | 3 | 4 | 12 | 15 | -3 | 12 |
| 8 | RostovRostov | 10 | 3 | 3 | 4 | 13 | 17 | -4 | 12 |
| 9 | Akron TolyattiAkron | 10 | 3 | 2 | 5 | 14 | 18 | -4 | 11 |
| 10 | Krylia SovetovKrylia Sovetov | 10 | 3 | 2 | 5 | 9 | 14 | -5 | 11 |
| 11 | Nizhny Novgorod | 10 | 3 | 1 | 6 | 9 | 19 | -10 | 10 |
| 12 | Dynamo MakhachkalaMakhachkala | 10 | 2 | 4 | 4 | 4 | 8 | -4 | 10 |
| 13 | KhimkiKhimki | 10 | 1 | 5 | 4 | 9 | 16 | -7 | 8 |
| 14 | OrenburgOrenburg | 10 | 1 | 4 | 5 | 12 | 19 | -7 | 7 |
| 15 | Akhmat GroznyAkhmat Grozny | 10 | 0 | 6 | 4 | 7 | 18 | -11 | 6 |
| 16 | Fakel | 10 | 1 | 3 | 6 | 4 | 17 | -13 | 6 |
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