The Denmark international keeper will move to England from current club Aalesunds in December, but will not be eligible to play until the transfer window opens.
United boss Sir Alex Ferguson expects Edwin van der Sar to retire from playing at the end of the season and is considering bringing in another keeper after being linked with the likes of Maarten Stekelenburg, Manuel Neuer and David De Gea.
He told VG: "I am not travelling to Manchester to sit on the bench and I feel that I am brought to the club to fight for a place in the starting XI.
"It's obvious that this is a dream. I have followed them since I was a small boy and my father is a big fan.
"For Manchester United, it's a long process to buy players and they have been tremendously careful. I feel they know me better than I do myself."