The 6ft 3in striker starred for Iceland in Euro 2016, scoring against Austria and started in the famous 2-1 victory over England.
Bodvarsson has signed a three-year contract and the fee is believed to be at least £1m.
He becomes Wolves fourth signing in just five days after the captures of Portuguese trio Helder Costa, Silvio and Joao Texeira.
QPR had been chasing the 24-year-old but Wolves are believed to have out-bid their Championship rivals, who came close to agreeing a £1m deal.
Bodvarsson only moved to Kaisterlautern from Viking in January, after a prolific run of nine in 14 games for the Norwegian side in 2015.
He netted twice in 15 games for the German second-tier club before his Euro 2016 exploits.