The Serbia international announced his decision to end his eight-year association with the club earlier on Friday.
Vidic has enjoyed a trophy-laden stint at Old Trafford winning domestic honours in the form of five Premier League titles and three League Cups, and extending that success to Europe by collecting the UEFA Champions League in 2008.
The 32-year-old has reportedly become disgruntled by the lack of progress on a new contract with the reigning champions, and has announced he will now ply his trade outside of England.
That decision has called into question his role as captain, but Moyes says that position will not change and insisted the decision to end his United stay was mutual.
"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."
When asked whether Vidic could lose focus after announcing his decision to leave, Moyes added: "No, not somebody like Vida. He's a great leader for this club and served the club really well and I would expect that to continue right up until the end of the season."
United take on Fulham at Old Trafford on Sunday, a fixture that sees Fulham head coach Rene Meulensteen return to a club he served under former boss Alex Ferguson.
Moyes revealed he wanted the Dutchman to stay on the coaching staff, but accepted his decision to move on.
"Rene helped me when I first came here," Moyes continued. "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."
