As expected, Steve Round will become Moyes' assistant manager, Chris Woods is installed as goalkeeping coach, with Jimmy Lumsden named coach.
"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," said Moyes.
The trio replace Mike Phelan, Rene Meulensteen and Eric Steele, who have all been released following Sir Alex Ferguson's decision to retire in May.
Round, 42, has worked alongside Moyes since 2008, whilst former England keeper Woods had been at Goodison Park since 1998.
Sixty-five-year-old Lumsden meanwhile, has worked with Moyes since his days at Preston North End.
Moyes added: "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.''
Moyes arrived at Carrington at 8am this morning for his first official day in charge, although his players are not due to report for duty until later this week.
It is a huge day of change at United.
In addition to Moyes' arrival, the Red Devils' plush training ground is officially known as the AON Training Complex as a result of a sponsorship deal announced last April worth approximately £150million.
David Gill's exit as chief executive means Richard Arnold now takes over as group managing director, with London-based executive vice-chairman Ed Woodward assuming many of Gill's responsibilities on the football side.
"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,'' Woodward said.
"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.''
It was also confirmed Woods would continue in his role as USA goalkeeping coach until next summer's World Cup.
However, the former England keeper will not be involved in this month's Gold
Cup qualifiers against Belize, Cuba and Costa Rica as it would have prevented him playing a full part in United's pre-season tour of the Far East and Australia.