The 23-year-old has agreed personal terms and joins on a five-year contract until 2017.
Man Utd boss Sir Alex Ferguson 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."
Buttner was part of Holland's preliminary squad for this year's European Championship and has made 119 appearances for Eredivisie side Vitesse over the past four years.
He becomes the second Dutch player in a week to make the switch to Manchester United, following in the footsteps of striker Robin van Persie, move moved from Arsenal in time to feature in last night's season-opening 1-0 defeat at Everton.
"Joining Manchester United is one of the best days of my life," Buttner said.
"It's a team I have admired for many years now and I can't wait to join my team-mates and play my part in helping the club be successful."
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The Dutchman completed his medical in Manchester on Tuesday and is understood to have moved on a deal worth £3.9 million.
Buttner, a product of the youth system at Vitesse, was linked with a move to Barclays Premier League newcomers Southampton earlier in the summer, but that deal fell through, paving the way for the switch to United.
Buttner will provide much-needed cover for first-choice left-back Patrice Evra.