The Denmark No 1 had attracted interest from Chelsea and Roma earlier this summer.
The 31-year-old joined from Leeds in 2011, playing a key role in Leicester’s promotion from the Sky Bet Championship in 2013/14 before playing every minute of their Premier League-winning campaign two years later. “I’m very happy to be here for many more years. I’ve spent the majority of my career at Leicester now and had some amazing times here, so hopefully we’ll have some more,” he told the club’s website. “I’ve felt at home at this club from day one, so I’d like to thank the fans for the support they’ve given me and also the owners who’ve played a huge part in my career. I want to bring more success to this club as I’ve loved every minute and hopefully we can keep going in the right direction.” The shotstopper, son of legendary Manchester United goalkeeper Peter, has kept 42 clean sheets in 136 Premier League appearances.