Kagel was born in Buenos Aires on 24 December 1931 into a polyglot Argentine-Jewish family with strongly leftist political views. He studied theory, singing, conducting, piano, cello and organ with private teachers, but as a composer was self-taught. At the University of Buenos Aires, where Jorge Luis Borges was among his lecturers, Kagel studied philosophy and literature. In 1949 he became artistic advisor to the Agrupacion Nueva Musica of Buenos Aires; he began composing in 1950, seeking musical ideas that opposed the neoclassical style dictated by the Peron government. After an unsuccessful attempt to establish an electronic studio, in 1955 he became chorus director and rehearsal accompanist at the Teatro Colon and editor on cinema and photography for the journal nueva vision
. In 1957 Kagel traveled to Germany on a DAAD student grant, settled in Cologne, and became immediately and permanently involved in the contemporary music network as a member of the so-called "second generation" of Darmstadt composers.
In Germany he participated in the Darmstadt summer courses (from 1958), where he later lectured (1960-66, 1972-76), and conducted the Rheinland Chamber Orchestra in contemporary music concerts (1957-61). Between 1961 and 1965, he also made several concert and lecture tours in the USA. In 1969 he was named director of the Institute of New Music at the Rheinische Musikschule in Cologne and, as Stockhausen's successor, of the Cologne courses in new music (until 1975); in 1974 he became professor of new music theater at the Musikhochschule in Cologne. Kagel was one of the founders of the Ensemble for New Music in Cologne and has worked at the electronic studios in Cologne, Berlin, and Utrecht. He continues to conduct many of his works and directs and produces all of his own films and radio plays.