The Denmark goalkeeper has made a big impression at Old Trafford and had become Sir Alex Ferguson's first choice until he suffered a serious ankle injury in January.
He has since returned to full fitness and will be part of the United squad that heads to Scandinavia for the next leg of their pre-season tour this weekend.
Ferguson said: "Anders is still relatively young for a goalkeeper, he has come on leaps and bounds since joining us last year."
The Red Devils boss added: "There is healthy competition in the goalkeeping department which is always good for the team, albeit a headache for me.
"I am delighted he has signed a new contract and also delighted to see that he has clearly returned from the summer break in good shape after the disappointment of suffering an injury last season."