The 32-year-old will join the Italian giants in the summer on a Bosman after eight years at Old Trafford.
"Nemanja has signed now and we are all happy for him," Martina told FC Inter News. "He's joining Inter with great enthusiasm and is looking forward to the start of a new adventure.
"He's been watching a lot of Italian games on television and is doing so with great interest."
Vidic has made 27 appearances for United so far this season.