The defender, who is in the last six months of his contract, confirmed that he wants to experience a new challenge and make the most of the rest of his career.
In a statement, Vidic said that his time at the club would always be the "best years of my career".
"It's the last year of my contract and I have had eight wonderful years here. My time at this great club will always rank as the best years of my career," he is quoted as saying by The Mirror.
"I never could have imagined winning 15 trophies and I will certainly never forget that fantastic night in Moscow, memories that will live with me and the fans forever.
"However, I have decided that I will move on at the end of this season. I want to challenge myself again and try to make the best of myself in the coming years."
Vidic also added that he will not join another English club, with Inter Milan reportedly the favourites for his signature.
"I'm not considering staying in England as the only club I ever wanted to play for here is Manchester United and I was lucky enough to be part of this club for so many years," Vidic continued.
"I've got a few options to move on and I will choose the right one for me and for my family."
Vidic joined United from Spartak Moscow in 2006.