The Old Trafford legend, speaking to Sky Sports News during a school visit as part of Sky Sports' Living for Sport programme, is also hopeful that Wayne Rooney will stay at Old Trafford.
Regarding Moyes' move to United, Beckham said: "I'm sure he has had lot of mentoring, he is one of those managers that has always picked up the phone and spoken to Sir Alex.
"It was always going to be diffcult job for whoever succeeded Sir Alex because of what the manager has brought to Mancester Utd, what he has brought to the game.
"But the same players are there and I'm sure a few more will be added over the next few weeks. Being manager of Man Utd is a great job."
Beckham believes it will be another thrilling year in the Premier League - and is confident that there will be first-time success for Moyes.
"It's going to be interesting this year as there have been so many changes throughout the Premier League," he added. "Jose is back and that's exciting. It's going to be interesting, but I still think United will win the league. I'm a Manchester United fan!"
Beckham believes the backroom changes at Old Trafford can only have a beneficial effect as the club looks to build on Sir Alex Ferguson's legacy.
"It's great about having a legacy and Manchester United have the biggest," he said. "Ryan Giggs has been there so many years and all the players look up to him. Phil Neville has gone back, such a talented person and coach.
"Obviously Gary Neville was involved in the club and Nicky Butt is involved with the reserves. So many of the young players respect them and look up to them. It's important to have that."
As to Wayne Rooney's future, Beckham said: "I hope he stays because Wayne is such a talented player and I see him as a Manchester United player.
"Obviously that'll be his decision and his decision only. As a Man Utd fan, I want to see the best players at the club and I hope he stays."