The 23-year-old, who was part of Holland's preliminary squad for this summer's European Championship, joins the Reds from Vitesse Arnhem, where he made 119 appearances over the past four years.
Sir Alex Ferguson said: "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."
Alexander Büttner said: "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."