The 25-year-old underwent a medical on Wednesday and the transfer, reported to be worth between £16million to £20million, has been finalised.
He becomes Sir Alex Ferguson's second signing of the summer after the capture of England Under-21 international Phil Jones from Blackburn for £16.5million.
"The opportunity to come and play for one of the biggest clubs in the world is one I couldn't turn down," Young told MUTV. "It's a chance to hopefully become part of the history by helping to win the 20th title.
"It's a prospect I always looked at from being a child - to play for one of the biggest clubs in the world.
"I've got that opportunity now so I've just got to take it with two hands."
Manager Sir Alex Ferguson will hope Young can play a key role as he begins overhauling the squad which won a record 19th title in May.
The forward scored 39 goals in 193 appearances but, significantly, in the last five Premier League seasons only Arsenal midfielder Cesc Fabregas has provided more assists.
Despite United finishing nine points clear of second-placed Chelsea last season, Ferguson always knew he would have to make changes to the playing staff.
The retirements of midfielder Paul Scholes, right-back Gary Neville and goalkeeper Edwin van der Sar left huge holes in terms of experience while other exits - such as defender Wes Brown - are expected.
Injury-plagued Owen Hargreaves' release this summer freed up another place in the squad while veteran midfielder Ryan Giggs will be 38 in November and centre-back Rio Ferdinand has struggled with his fitness over the last couple of years.
To that end the Red Devils boss has moved quickly in the transfer market by bringing in two of England's brightest talents.
In doing so he has also stolen a march on arch-rival Kenny Dalglish at Liverpool, who was interested in both Young and Jones.
The spending will not stop there, however, as next on the list is the replacement for Van der Sar.
It seems likely Atletico Madrid goalkeeper David De Gea will be the one to fill that key position, with Ferguson revealing a few weeks ago United had been working on the transfer for some time.
The 69-year-old Scot is also keen to add more creativity to his midfield as, despite comfortably winning the 12th Barclays Premier League title of his tenure at Old Trafford, his side were comprehensively outplayed by Barcelona in last month's Champions League final at Wembley.
United have been linked with both Udinese winger Alexis Sanchez - although Barcelona still seem favourites to clinch that deal - and Inter Milan midfielder Wesley Sneijder.
Villa, who signed Young from Watford in January 2007 in a deal eventually worth £10million, were resigned to losing one of their prize assets as he had only a year left on his contract and had made it clear he was not interested in renewing it.
"Ashley has made a terrific contribution for Villa over the past four-and-a-half seasons and everyone at the club wishes him the best for the future," said new Villa boss Alex McLeish.
"He has become an important player in the England team during that time and I'm sure he will be looking forward to this new challenge."