Cork was out of contract at the end of the month, but has agreed fresh terms, and can’t wait for an exciting new dawn at the club.
But the challenge now is to bounce back with a new boss after relegation, and Cork said: "I'm really excited to go again.
"There is an exciting opportunity to try and get promoted out of a tough league, and as soon as there was talks about extending my stay here, I couldn't wait to sign.
"The chance to work with Vincent Kompany, someone I have played against for a number of years, and someone who has won everything as a player, is great, and it will be great to learn from him.
"I can't wait, it's a new challenge and a new feel around the place.
"Burnley feels like home for me, the two spells I've had here have been great.
"I have made some great memories and hopefully we can make some more now."