Vidic announced on Thursday night that he would be leaving the reigning Premier League champions after eight seasons at the club.
"It was something that we all mutually agreed together," the United boss said.
"I think it was the right decision for club and player."
Vidic has been heavily linked with a move to Inter Milan.
The Serb will skipper the Red Devils until the end of the season.
"He has been a brilliant servant for Manchester United," Moyes added.
"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."
Moyes confirmed that Jonny Evans will miss Sunday's home game against Fulham with a calf injury he suffered against Stoke.
Phil Jones, who came off with concussion against the Potters, could be fit, however.
Marouane Fellaini's bad luck with injuries continues as he has suffered a groin injury and will be out for a week, Moyes added.
This weekend will be the first time that Fulham manager Rene Meulensteen has come back to Old Trafford since leaving the United coaching staff in the summer.
Moyes opted to bring in a number of his own staff when he replaced Sir Alex Ferguson as manager.
The former Everton boss revealed he was sad to see the Dutch coach leave United, however.
"Rene helped me when I first came here," Moyes said.
"I had several conversations with him. He helped me, told me about the club, how it runs and the players.
"In the end I would have liked him to stay at the time but he wanted to go and that was fine.
"I am looking forward to getting Rene back and seeing him."
Meulensteen has struggled at Craven Cottage since replacing Martin Jol last December.
Under the Dutchman, who has very limited managerial experience, Fulham have sunk to the foot of the Barclays Premier League.
The pressure on Meulensteen intensified on Tuesday when the Londoners were knocked out of the FA Cup by Sky Bet League One strugglers Sheffield United.
Moyes admits he feels sorry that talk has already begun about Meulensteen potentially losing his job after only two months at the helm.
"There's always disappointment when you see a manager lose his job, because it's a difficult job. You have to have very good owners and chairman," said the Scot.
"I've been really fortunate here that I've got great owners and a great board, I had the same at Everton and at Preston.
"Unfortunately some of those other managers have not had the same privileges I've had.
"But it's part of the job and you realise you have to work with the people who employ you and unfortunately some of them haven't had as good ones as I've had."
Moyes has faced questions - from outside United - about his ability to bring the glory days back to Old Trafford following Ferguson's exit.
The champions sit some 15 points behind leaders Arsenal in seventh place.
Moyes is refusing to write off the title, but he admits the chances of retaining the championship are slim.
Moyes said: "What we'll do is keep trying to win the next game. If we can do that we'll see where we go.
"We need teams to slip up if we are to have any chance."