The 32-year-old, who has already been linked with a move to Inter Milan, will remain as United's captain for the remainder of the season.
And 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."
United will be without injured duo Johnny Evans and Marouane Feillaini for Sunday's game against bottom-of-the-table Fulham, but Phil Jones could be available despite suffering a head injury against Stoke last weekend.
The game will mark Fulham manager Rene Meulensteen's first visit to Old Trafford since leaving the club's coaching staff in the summer and Moyes is delighted to welcome him back.
"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."