Swedish composer and organist, born January 21, 1920 in Höör, died September 24, 1999 in Stockholm.

He was the son of cantor Torsten Nilsson.

Nilsson studied at the Stockholm Conservatory of Music 1938-1943. He was organist in Köping's Church 1943-1953, in St. Mary's Church in Helsingborg 1953-1962, studied for Anton Heiller in Vienna 1961 and 1963, was cantor and choir leader in Oscarskyrkan 1962-1977, organist there 1977-82 and head of music at the State Historical museum 1983-84 He was a teacher of liturgical singing at Uppsala University 1965-1970, at the Stockholm Theological Institute 1965-1970 and in music theory at the Stockholm Municipal Music Institute 1967-77.

There is also a violinist Torsten Nilsson (3) with the same name.