The 23-year old Dutch left-back has now completed his medical with the Red Devils and has signed a five-year deal which has delighted manager Sir Alex Ferguson.
"Alexander is one of the best young left-backs in Europe and we're delighted to sign him," Ferguson told the club's official website.
"He's someone we've been watching for a while now. He gives us some really exciting options in that position."
"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."