Arsenal legend Graham backing Moyes for Man Utd success
But it is Moyes' appointment that looks the most demanding, as he steps into the shadow cast by Sir Alex Ferguson.
Graham told the Mirror: "It is the natural progression in his career. He has served his time as an apprentice at Preston and then at Everton - where he did a brilliant job. I believe he is the perfect choice to take over.
"United could have turned to a foreign manager, but I am glad they stayed British.
"There are a lot of similarities between Moyes and Sir Alex.
"Moyes has the same hunger and ambition - and he has that drive that is so common from people from the west of Scotland.
"He has drive to be successful. He is also a realist and knows there will be inevitable comparisons between him and Sir Alex, especially if United lose a few games.
"But he will ready for that. He will be prepared - and it will not concern him about handling big names.
"There were star players at Everton when he first arrived. It won't be a problem for him. He will relish the challenge and it would be no surprise to me if he won the title next season."