The 50-year-old, who spent 11 years in charge at Everton, was brought in swiftly to replace Sir Alex Ferguson following his decision to retire in May.
And although Irwin believes United with face a difficult task in retaining their Premier League title, he has backed Moyes to lead the club to glory.
“Of course he [Moyes] can succeed,” Irwin told Goal.
“He has the players there who won the league last year, so they have plenty of experience, like Rio [Ferdinand], and a good blend of youth as well.
“No doubt he’ll put his own stamp on his ideas, his philosophy and the way he wants to play football and will probably make a couple of his own signings.
“It will be interesting next year; it will be a tough year because of the new managers at Chelsea and Manchester City. But I don’t see a reason why they can’t succeed.”
The Red Devils open their title defence with an away trip to the Liberty Stadium against Swansea City on August 17 before hosting Chelsea seven days later.