Cardiff's Premier League debut season will be Gunnarsson's fourth with the club since making the move from Coventry City.
He told the Western Mail: "It was a great decision to sign for Cardiff. I have dreamed of playing Premier League football since I was a boy in Iceland and promotion has given me that chance.
"Quite a few Icelandic players have been in the Premier League, Gudjonsson, Hreidarsson and more. They are all good friends of mine and they tell me it's the best league in the World.
"Next season I will find out for myself. I want to be a part of that."