The Red Devils have confirmed the highly-rated midfielder has already passed a medical and agreed a four-year contract which will start July 1.
Powell attracted the interest with a number of sparkling displays for Crewe in League Two, netting 14 goals in 38 league appearances last season to help the club secure promotion.
Speaking to the club's official website, Sir Alex Ferguson said: “We have scouted Nick for months now. He is an exceptional talent and has been schooled well at Crewe.
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United are thought to have beaten of competition from a number of their Premier League rivals including Everton, Arsenal and Chelsea to sign the youngster.
The 18-year-old, is delighted to have completed his "dream" move and is looking forward to playing alongside his new team-mates next season.
He 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.”
Powell is the second arrival at Old Trafford after the club confirmed a deal is in place to sign Shinji Kagawa from Borussia Dortmund.