Starting his career in Degerfors IF, a club known to produce many young talents, Edström moved to Åtvidabergs FF and became national champion in 1972.
Edström made 40 appearances for the Swedish national team and scored 15 times. He is most noted for his performance in the 1974 FIFA World Cup where had a big part in Sweden finishing fifth, and he made 6 appearances during this tournament.
On club level, he became not only Swedish Champion, but also Dutch (twice) and French Champion. He also won the Swedish, Dutch and Belgian Cups and was voted Swedish player of the year twice (1972 and 1974, winning Guldbollen).
He has been an expert radio commentator since the 1980s.