Widely regarded as the best center forward in the world after a string of impressive performances for the Sweden national team, Simonsson was signed by the La Liga team Real Madrid in 1960. However, fierce competition from especially Alfredo Di Stéfano limited Simonsson's playing chances at the club and he ended up playing in only 3 league games during the 1960–61 La Liga season, scoring one goal as Real Madrid was crowned champions. He was also a part of the Real Madrid teams that won the 1960 Intercontinental Cup and the 1962–63 La Liga, but did receive any playing time. As of 2020, Simonsson is still the only Swede ever to have represented Real Madrid.