The commanding Serbian centre-back has been with United since January 2006 but he will leave for Italian side Inter Milan at the end of the current season.
Asked when he decided to leave, Vidic told Sky Sports: "It was as late as January. Like the manager (David Moyes) has said, it was a mutual decision.
"Sometimes, you have to accept it is time for a change. Time to fight for different things, to have a different challenge - and that is definitely going to happen in Italy."
Sir Alex Ferguson's remarkable stint in charge of United finally came to an end at the conclusion of last season but Vidic says his old manager's departure was not a factor in his decision to leave.
"Not at all," he said. "It's just something that has happened as the season has gone on.
"Following a conversation with the manager, it happened that I decided to change leagues and play in a different country."
Vidic agreed that the next months could be emotional, adding: "I am starting to think about how long I have left at the club.
"I see a lot of people on the street and they still have appreciation for what I have done for the club.
"Sometimes, it's hard to listen to these comments, but that's football, that's life. You have to accept that's how things go and move on.
"I would like to finish on a high and finish with good performances. I'm looking forward to playing every game I possibly can."
Vidic has enjoyed huge success in his time at United but the current campaign has not been so successful and they were only seventh in the table heading into Sunday's game with Liverpool.
But Vidic says the club are still hopeful of claiming a top-four finish and thinks they have every chance of recovering from 2-0 down in their Champions League last-16 tie against Olympiakos.
"We changed manager, we changed director, the club is going through transition," said Vidic.
"The manager wants to build his team, his way of playing and, to achieve that, you need time.
"I knew it was going to be a hard season but I am surprised how it has gone. Hopefully, we can turn it around.
"I'd rather be 2-0 down and then play Olympiakos at Old Trafford than have beaten Barcelona 1-0 and then have to go to the Nou Camp. I think we have a big chance to go through."
Asked whether he thought a top-four finish was still attainable, he said: "I still believe and we have to believe. It is going to be tough but things can change."
Reflecting on his career at United in general, Vidic said: "It has been a great eight years, or a great seven years because at the moment we are not doing so well!
"I have great memories. To win five titles and the Champions League, I couldn't dream of winning that many titles and of playing with so many great players.
"I have learned a lot, not just on the pitch but off the pitch as well.
"I have been playing for the greatest manager ever, I believe. It was a great experience and, as I said once before, this is going to be the best part of my career, these years with United."
Asked for his favourite memory from his time at the club, Vidic did not hesitate, saying: "The Champions League final (in 2008 against Chelsea, which United won 6-5 on penalties.
"You don't win the Champions League every year. The club has won it three times and I was lucky to be part of a team who won it once.
"And we won it Moscow, where I played for Spartak for one-and-a-half years. I came back to the stadium to lift the trophy and that's the greatest memory I have."
Vidic will treasure his years in England and added: "Manchester United make you feel part of the family. I have developed as a man at this club, it has been a great experience for me and my family.
"I have nothing to regret, I have given 100 per cent."