Speaking after arriving at Molineux, Bodvarsson said: "It's a club with great ambition, a good history and fantastic facilities so, when that all fits in, then it's an easy decision and I'm really, really happy.
"There's been a lot of dialogue between Wolves and Kaiserslautern, so obviously it's been a little chaotic, but the clubs have come to agreement and now I can't wait to start.
"I grew up watching the Premier League and the Championship. English football is very popular in Iceland so it's been a great ambition of mine to play in English football.
"I like the style of play and there's something about the football that's always attracted me.
"Wolves is a club that I've always known about, I remember watching them in the Premier League.
"I know what kind of club Wolves is, it's a really attractive club with great and high ambitions.
"They want to be at the top level, I know it will take time but hopefully we can get there as soon as possible."
Jon Dadi Bodvarsson was one of the key figures in Iceland’s impressive run in this summer’s European Championships in France.
He started all five of Iceland’s fixtures, including the win against England, and scored the opening goal in the group victory against Austria.
"It was unbelievable. We managed to surprise a lot of people as well as ourselves. I'm just really grateful for having that experience," he said.
"Not every player gets that opportunity in his career and to go that far was unbelievable."
In total he boasts 25 caps having come through the ranks for Iceland’s Under-19s and Under-21s.
He began his club career with UMF Selfoss in the Icelandic League before joining Viking FK in the Tippeligaen – the top division in Norway - in 2013.
From there he joined Kaiserslautern in Bundesliga 2.
In his career so far he has notched 27 goals from 139 games, and his physique and 6ft 3in frame allows him to be an effective foil for those players around him.