Vidic will play for Inter Milan next season, the Italian club have announced.
Inter president Erick Thohir told inter.it: "Vidic is a world-class player. I'm extremely happy to have completed this deal to bring Nemanja to Milan. He's one of the world's best defenders and his qualities, international pedigree and charisma will be an asset to the team and help bring through our younger players.
"He will bring added value to the club and is another piece of the great Inter side we are building. I would also like to take this opportunity to thank Manchester United, Nemanja and his entourage for the professional and cooperative approach they have shown throughout the negotiations."
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