The Serbia defender has enjoyed a hugely successful career at Old Trafford since joining from Spartak Moscow in 2006, helping the club win a string of trophies.
But Vidic's contract runs out in the summer and he will seek out a fresh challenge, with Inter Milan thought to be favourites to sign the 32-year-old.
Injuries have restricted Vidic's appearances in recent years and he featured in just 23 games last season, but the centre-back has been a regular starter in United's defence this campaign.
He becomes the latest long-serving player to announce their departure and it remains to be seen if he will be followed by Patrice Evra, Rio Ferdinand and Ryan Giggs, who are all out of contract in the near future.
A statement from Vidic on Manchester United's official website read: "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.
"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.
"I've got a few options to move on and I will choose the right one for me and for my family.
"I am now going to focus all my efforts on playing for Manchester United and do the best I can for the team until the end of the season.
"I hope this stops any further speculation about my future."
Manager David Moyes insists he will continue to rely upon the 6ft 2in centre-back as United try to force their way back into top-four contention this season.
"It was something that we all mutually agreed together," Moyes said. "I think it was the right decision for club and player.
"He has been a brilliant servant for Manchester United. He is captain and it will remain that way until the end of the season.
"He has been a great player for us and we will continue using him."
While Moyes has spoken about the positive influence Vidic still has at United and indicated he wanted him to stay, it is not thought he was offered an extension and he has now decided to move on.
Vidic is free to talk with clubs outside England under the Bosman regulations, with Inter believed to be one of the front-runners to acquire his services.
The 32-year-old has been one of the most popular members of the Red Devils' squad since he arrived from Spartak for £7million - a transfer bizarrely announced on Christmas Day in 2005.
He has played a central role in virtually all United's significant triumphs since then - Vidic did recently reveal he handed his first winners' medal from the 2006 Carling Cup to Giuseppe Rossi as the Italian had played in all the previous matches up to the final.
Last May, Vidic skippered United to their historic 20th championship - his fifth and the last under Sir Alex Ferguson.
However, the tough defender made only 19 league appearances as he battled to overcome a serious knee injury, suffered in a Champions League defeat to Basle in December 2011 that required two major operations, ruling Vidic out for extended periods on both occasions.
The Champions League triumph over Chelsea at the Luzhniki Stadium in 2008 remains the high point of Vidic's entire career, given he subsequently featured in the final defeats to Barcelona in both 2009 and 2011, by which time the former Red Star Belgrade man had been elevated to captain.
Vidic's overall contribution is underlined by his presence in the PFA Premier League team of the season on four occasions and the FIFPro World XI twice.