The Argentine will spend the next season with Massimiliano Allegri's side after a frustrating campaign with the Nerazzurri last term
The 28-year-old joined the Nerazzurri from Palermo last season, but failed to nail down a regular starting spot for the club.
Milan, meanwhile, are in need of defensive reinforcements following the injury sustained by Daniele Bonera, confirming their interest in the Argentine shortly afterwards.
It had looked as though his cross-city move had been called off but the Rossoneri soon revived their interest and have got their man for the next year with an option of buying him.
"Inter announce that the Argentine defender Matias Silvestre has been transferred to AC Milan on loan with an option to buy," a Nerazzurri statement read.
The centre-back began his career at Boca Juniors and first made the move to Serie A back in 2008, when he joined Catania.
He spent three years at the Angelo Massimino before moving to their Sicilian rivals and earned a €6 million [£5.2m] move to San Siro a year later.