Davis believes that the talented 18-year-old has the ability to develop into one of the top players in the country and feels that signing for United will only assist in his continuation in becoming a future England International.
Davis told the club's official web-site: "Nick has shown everyone what a talent he possesses. He got better as the season went on and played a vital role in us winning promotion.
"He is a match winner and was deservedly named as our player-of-the-season for the contribution he made. He has added goals to his game and I think he will only continue to improve and develop at a top club like Manchester United.
"If he can continue to progress then there is no reason why he cannot become the top player we all believe he can be.
"Everyone at Crewe Alexandra is delighted that Nick has signed for Manchester United and we are pleased for him. I would like to personally thank him for helping us win promotion last season and we all wish him all the very best for the future.
He added: "I'm sure our supporters will now follow his progress with great interest."