The 34-year-old, who recently retired from international football in an aim to prolong his Old Trafford career, signed a one-year deal on Thursday.
And Moyes, who replaces retiring boss Sir Alex Ferguson, is thrilled he will be able to call on the services of the experienced centre-back, whose old deal was due to expire at the end of the season.
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"Even from the outside you can see what a big character Rio is around the dressing room. I am delighted he has signed a new contract and I am looking forward to working with him."
The 2012-13 season was one of the best of Ferdinand's career, with the former England international being named in the Premier League team of the season as well as picking up his sixth league title, and there are no signs he is done yet.
When asked about about the deal, Ferdinand said: "Who wouldn't want to play in this fantastic team in front of 75,000 fans every week. It has been an incredible journey and I am glad it will continue.
"I can now fully concentrate on my club career, which has worked well for me over the past few years. This is a great team to be part of and we are now moving into a new era, which is very exciting.
"I have met with David Moyes and I am really looking forward to working with him and winning many more trophies with this great club."