The 23-year-old midfielder plays his club football for Rubin Kazan but has been regularly linked with a move to the Serie A giants.
Reports in the Italian media suggest the player arrived in Milan on a flight on Tuesday evening.
"I am here for Inter," M'Vila is quoted as saying in Corriere dello Sport.
M'Vila made 32 appearances for Rubin in all competitions last term.
The France international joined the Russian club from Rennes a fee of £9.6 million in January last year.
He was linked with the likes of Fulham and QPR before signing for Rubin.
M'Vila was not included in Didier Deschamps' squad for the 2014 FIFA World Cup in Brazil.
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