Nordahl was born into a family footballers. His brothers Bertil, Gunnar and the twins Gösta and Göran also played in the highest Swedish league.
In the 1940s he played for IFK Norrköping, with whom he became Swedish champion several times. In 1950 he moved as many Swedes to Italy. He signed with AS Roma, where he played with his countrymen Stig Sundqvist and Sune Andersson.
Nordahl played 1945-1950 26 times for the Swedish national team and was able to score a goal. In 1948, he won the gold medal at the Olympics, his brothers Gunnar and Bertil were also in the squad. Two years later he succeeded with the selection of third place in the World Cup 1950. After his move to Italy, he is no longer included in the national selection, as the Swedish Football Association at the time refused to professional football.