The 23-year-old, who had been playing for Vitesse Arnhem, arrived in Manchester yesterday afternoon for talks over personal terms and a medical examination.
Those talks were successful and the defender has now committed his future to the Red Devils.
"Joining Manchester United is one of the best days of my life," he told the club's official website. "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."
Manager Sir Alex Ferguson added: "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 could now make his debut during Saturday's Premier League encounter against Fulham.