United beat competition from the likes of Chelsea, Arsenal and Manchester City who were also targeting the youngster. Powell signed a four-year-deal with the club and is United's second signing after the unveiling of Japan's Shinji Kagawa from Dortmund.
Powell was named the player of the season after the 18-year-old scored 16 goals in 45 appearances.
"We have scouted Nick for months now. He is an exceptional talent and has been schooled well at Crewe. I'm delighted he has chosen to come to United. He has a lot to offer and we are all looking forward to working with him," manager Alex Ferguson told the club's official website.
Powell said that it was a dream come true and thanked his previous employers for his development as a player.
"It really is a dream come true to be signing for Manchester United. I have had a great time at Crewe and I would like to thank them for helping me to develop as a player over the past 13 years, said Powell.
"I'm excited about continuing my development with Sir Alex and the world-class players in the squad. The thought of making the step up to the Premier League next season is an exciting prospect. I can't wait to get started."