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 | 15 | 11 | 4 | 0 | 32 | 7 | 25 | 37 |
| 2 | Zenit St PetersburgZenit | 15 | 11 | 3 | 1 | 33 | 7 | 26 | 36 |
| 3 | Lokomotiv MoscowLokomotiv | 15 | 11 | 1 | 3 | 30 | 18 | 12 | 34 |
| 4 | Dynamo Moscow | 15 | 9 | 3 | 3 | 31 | 17 | 14 | 30 |
| 5 | Spartak Moscow | 15 | 8 | 4 | 3 | 25 | 12 | 13 | 28 |
| 6 | CSKA MoscowCSKA | 15 | 8 | 3 | 4 | 24 | 10 | 14 | 27 |
| 7 | Rubin Kazan | 15 | 5 | 4 | 6 | 17 | 22 | -5 | 19 |
| 8 | RostovRostov | 15 | 4 | 5 | 6 | 20 | 26 | -6 | 17 |
| 9 | Akron TolyattiAkron | 15 | 4 | 4 | 7 | 19 | 30 | -11 | 16 |
| 10 | Nizhny Novgorod | 15 | 4 | 3 | 8 | 15 | 27 | -12 | 15 |
| 11 | Dynamo MakhachkalaMakhachkala | 15 | 3 | 6 | 6 | 9 | 14 | -5 | 15 |
| 12 | Krylia SovetovKrylia Sovetov | 15 | 3 | 3 | 9 | 13 | 23 | -10 | 12 |
| 13 | KhimkiKhimki | 15 | 2 | 6 | 7 | 16 | 28 | -12 | 12 |
| 14 | Fakel | 15 | 2 | 6 | 7 | 10 | 23 | -13 | 12 |
| 15 | Akhmat GroznyAkhmat Grozny | 15 | 1 | 6 | 8 | 13 | 29 | -16 | 9 |
| 16 | OrenburgOrenburg | 15 | 1 | 5 | 9 | 16 | 30 | -14 | 8 |
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