The Premier League champions, who are now officially under new management following Sir Alex Ferguson's retirement, have confirmed that Moyes has brought his right-hand men from Everton with him to Old Trafford.
Moyes told the club's official website: "I have worked with Steve, Chris and Jimmy for a number of years and I am delighted they have decided to join me at this great club.
"They bring great qualities in their respective fields and I know that, like me, they feel that this is a challenge to relish. I have great faith that together, we can build upon the success this club has enjoyed over many years."
Executive vice-chairman Ed Woodward added: "I believe with David and his new team in place, along with our current backroom staff, we can now start preparing for the new season ahead. This is an exciting and challenging time for the club and I have great belief that David and his team will have all the energy and attributes needed to help this club continue in its long-standing traditions."
Meanwhile, widespread reports have claimed that Moyes's first task will be to sort out the future of unsettled striker Wayne Rooney.