The Scot has brought three of his long-term allies with him as he arrives at Carrington to start work as Sir Alex Ferguson's replacement.
Moyes arrived at Carrington - now officially renamed the AON Training Complex - on Monday morning to start work as Sir Alex Ferguson's successor, and the Premier League champions have wasted little time in announcing his backroom staff.
As well as Round, who has worked with Moyes since 2008, Chris Woods has been named goalkeeping coach while Jimmy Lumsden has also been handed a role behind the scenes.
"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," Moyes said.
"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."
Woods also serves as the U.S. goalkeeping coach and it remains to be seen if his new role will affect his international job.
Chief Executive Ed Woodward, who has taken over from David Gill, 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."