The Denmark goalkeeper penned a new deal last week to 2023.
“It is a club that has made me feel at home from day one," he said.
“I came on the back of a tough time at Leeds and from day one from when I stepped into this club everyone made me feel so welcome.
“We have achieved a lot together. It has been one hell of a ride, more than I could ever have expected.
“Leicester has done so much for me and I just want to keep repaying the fans and the owners in particular because they have looked after me and my family so well.
“There is nothing they won't do for anyone at the club. It is a great thing, to be part of a club that treats people like family.
“They make sure that everyone is feeling good and pushing in the right direction.
“The club is heading in a great direction. There is a new training ground coming soon, they are redeveloping the stadium, all these things are signs the club is heading in the right direction.
“The club is going in a good direction and I wanted to be part of that."