Cork told the club's website: "The club has been such a big part of my life for 14 years now. Both my kids are Burnley fans. It will always be a club that we're close to. It's gone so fast it's been some journey.
I just want to say a massive thank you to the fans. They've been amazing to me since I've been here. They've made me feel at home, made me feel so welcome from the start. Everyone at the club has been amazing with us.
I'm looking forward to the next adventure but I don't know how I'll feel on Sunday. It'll be nice to get to say goodbye to everyone. Everyone has been so good to us on the journey."
Gudmundsson also said: It's been a massive part of my career and I've enjoyed every single year. To play the last game at Turf Moor will mean a lot to me. I'm really going to miss this club.
It's been the best time of my football time for sure. To be part of the history we've created over the last few years has been incredible. I really hope this club goes back to the Premier League because, in my mind, they should be there."