Gudmundsson joined Burnley from Charlton Athletic in the summer of 2016, and had one year left to run on his contract with the Premier League outfit.
The 27-year-old has now penned a fresh three-year deal at Turf Moor, however, and has revealed that he is looking forward to playing in the Europa League for the club next season.
"This season has been a good season for myself and the team and being rewarded with a new contract is a great thing," Gudmundsson told Clarets Player HD.
"It's something I wanted to do. I want to stay here. I feel comfortable here and my family likes it here, so I definitely wanted to sign a new contract. It's a good thing to sign it before the World Cup, just to get everything out of the way and now I can concentrate on the last game and the World Cup.
"I think I've played well this season but as a player you always want to do better and next season I will hopefully do even better. I have a few good years probably in me.
"I'm at a great age at the moment and I think there are better things to come from me. They are exciting times and it's going to be nice to play in Europe."
Gudmundsson has scored twice and registered eight assists in 34 Premier League appearances this season.