The 23-year-old has signed a five-year contract and is expected to be officially unveiled as a Manchester United player on Friday after completing a medical on Tuesday.
"Alexander is one of the best young left backs in Europe and we're delighted to sign him," Sir Alex Ferguson told manutd.com. "He's someone we've been watching for a while now. He gives us some really exciting options in that position."
Ferguson has been striving to sign reinforcements at left-back all summer and had initially been linked with a move for Everton's Leighton Baines.
This, however, never transpired and United also missed out on the signing of Spain international Jordi Alba, who left Valencia to join Barcelona last month.
Few would have predicted that Buttner would be the next player on the radar of the Red Devils, and the news of Manchester United's interest even came as a surprise in the Netherlands.
In July, Buttner had a medical ahead of a move to Premier League newcomers Southampton and expressed clear delight at the opportunity to join the south coast club.
This move, however, fell through after negotiations between the clubs broke down, and United have pounced to ensure Buttner will be moving to England after all.