Blomdahl initially studied biochemistry, later he was a pupil of Hilding Rosenberg. He was heavily influenced by Paul Hindemith and was a member of the Monday Group. From 1960 to 1964 he was professor of composition at the Royal Swedish Academy of Music, then he held from 1965 to 1968 when Swedish Radio, the position of music bosses.
His compositions next three symphonies, concertos, operas and chamber music including electronic and experimental music. He wrote the music for the space opera Aniara. For this he was in 1965 awarded the Music Prize of the Nordic Council. The text was written by Erik Lindegren, who was inspired by the book by Harry Martinson. The premiere took place at the Hamburg State Opera in 1959. Blomdahl also composed the opera Lord of Hancken, the text of which also came from Erik Lindegren, inspired by Hjalmar Bergman. The premiere took place in 1965 in Stockholm.