Bäck studied at the Royal Music Academy of Stockholm and also studied composition with Rosenberg. As Rosenberg's student, Bäck developed a style in which melody is the essential element. He composed in a twelve-tone method with the lyrical style of Webern. Many of his works are religious in nature and he is known as one of the major contributors to contemporary liturgical music. He has also composed for stage, orchestra voice, and chamber groups. Bäck turned to electronic music in the 1970s and has since composed extensively in that area.