The 18-year-old has signed a four-year contract after a passing a medical and joins United for an undisclosed fee.
Sir Alex Ferguson told United’s official website: “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.”
Powell said: “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.
“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.”