Nordahl was born into a family footballers. His younger brothers Knut, Gunnar and the twins Gösta and Göran also played in the highest Swedish league, partly abroad.
Nordahl began his career in his hometown at Hörnefors IF. There they became aware of the technically gifted players and in 1942 he moved to Degerfors IF. In 1949 he went to Italy to Atalanta. In 1952 he returned to Sweden to Degerfors IF, where he also finished his career.
1945 Nordahl debuted in the Swedish national team. In 1948 he took part with the selection of the Olympic Games and won with the team the gold medal. His brothers Knut and Gunnar stood by him on the court. Because of his move to Italy, he was not allowed to play as a professional player in 1949 for the national team and thus came to only 15 international appearances.
After the end of his active career Nordahl moved to the dugout. He supervised, among other Örebro SK and IK Brage.