The 25-year-old will be heading to Leicester City where he will join Sven Goran Eriksson, who formerly managed him at both Manchester City and Nottingham County.
Danish Schmeichel, who joined on free transfer from Notts County last season, had a year to run on his contract.
“We feel this is the right deal for the club,” said Leeds manager Simon Grayson. “We spoke to Kasper’s agent at the end of the season about a contract extension and it was apparent that it was going to be difficult to agree a deal.
“Given the fact he has one year remaining on his contract we feel this is in the best interests of Leeds United.”
The move leaves the Whites with problems in goal after 34-year-old keeper Shane Higgs was released last month. He had made seven appearances last season.