The Dutchman becomes Sir Alex Ferguson's fourth signing of the summer, following the acquisitions of Shinji Kagawa, Nick Powell and Robin van Persie.
As Goal.com exclusively revealed last month, the Red Devils had initially targeted Everton defender Leighton Baines to fill the left-back slot, but the Toffees' asking price eventually led them to seek more a modestly priced alternative.
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Buttner has been capped by Netherlands up to the Under-20 age group and was part of Bert van Marwijk's preliminary squad for of Euro 2012.
Following confirmation of the deal, Sir Alex told the club's official website: "Alexander is one of the best young left-backs in Europe and we're delighted to sign him.
"He's someone we've been watching for a while now. He gives us some really exciting options in that position."
The former Ajax youth product also expressed his delight at making the move to Old Trafford, saying: "Joining Manchester United is one of the best days of my life.
"It's a team I have admired for many years now and I can't wait to join my teammates and play my part in helping the club be successful."