Torsten Nilsson studied at the State Academy of Music, Stockholm 1938-1942, graduating as a church musician and music teacher. He continued his studies with Anton Heiler in Vienna (composition and the organ, 1961 and 1965). As an organist he was also a pupil of Alf Linder. He was organist in Kšping 1943-1953, of St. Mary's Church, Helsingborg, 1953-1962, and was appointed organist of Oscar parish, Stockholm, in 1962, resigning from this appointment in 1979. He was also the director of the Oscar Motet Choir until 1984. He was Teacher of liturgical singing at Uppsala University, 1966-1970, and at the Stockholm Theological Institute, 1964-1970. He was also teacher of music theory at the Stockholm Citizens' School 1962-1973.

Where Torsten Nilsson is concerned, music does not have any single fount, its sources of inspiration being varied and complicated. Beauty, sensualism and eroticism have their contentious antitheses in anguish, paralysis and fear of death. In character his music often comes close to the scream of desperation, and the masterly composer for the organ has also developed an abundant vocal language. His melodies also glide into elevated, sensuously warm atmospheres. His intense, orgiastic imagination is reflected by the culmination of his music in ecstatic outbursts of sound and dance-like climaxes.