Paul Dessau was born in Hamburg on 19 December 1894. His grandfather was a synagogue cantor. He first took up violin lessons at the age of 6, and from 1910 to 1912 he attended the Klindworth-Scharwenka Conservatory.  Afterwards he chose conducting as his career and in 1912 he started at the Hamburg City Theatre as a vocal coach. From 1919, among other theatre engagements, he was engaged by Otto Klemperer at the Cologne Opera, and later moved to the City Opera in Berlin under Bruno Walter.

Meanwhile his composing career also produced an abundance of works. Soon he was attracted by the new medium, film, and started a prominent career as music director at various film theatres. During this period, he strove to bring new music and sound techniques into film. His first experiment in sound movies, Episode, entered the 1929 Baden-Baden festival, where he had met Bertolt Brecht for the first time two years before. While his major output was film music, there were also concert pieces as well as works for proletarian children's choirs.

In 1933 he emigrated to Paris, earning a living by composing music for other émigré film directors from Germany. In 1936, he met René Leibowitz and started to study the 12-tone system. As the Spanish Civil War broke out, he composed such political marching songs as Thälmannkolonne to the text by his wife Gudrun Kabisch (both under pseudonyms). This exile period also saw his attempts in compositions with Jewish themes as he struggled to find the root of his religious background. In 1938 he composed music for the Paris performance of the Brecht play Fear and Misery in the Third Reich (then titled 99%) which was directed by Slatan Dudow.

The next year he moved to New York. In 1943, Dessau met Brecht again on the occasion of an anti-Nazi concert where his 1936 song Kampflied der schwarzen Strohhüte was included on the program. In October 1943, he moved to Hollywood. In addition to close contact with Arnold Schönberg, he mainly composed or arranged orchestration for movie studios. A new phase began in his career as he again collaborated with Brecht in various projects. He was now more committed to political causes, which led to his joining of the US Communist Party in 1946.
In 1948, he returned to Germany. In 1951 his music for the opera Das Verhör des Lukullus (The Questioning of Lukullus) was charged following the Berlin premiere with formalism when socialist realism was held as the official principle in the GDR. After close discussions with Brecht, and after changing parts of the scripts, especially the final scene and subsequently, the title into Die Verurteilung des Lukullus (The Trial of Lukullus) to avoid misinterpretation, the newly revised opera received its official Berlin premiere in October of the same year. Then, it was not performed until 1960.

In 1952 Dessau was elected member of the Akademie der Künste and was now enthusiastically involved in music education for school-age children. The next major project in theatre The Caucasian Chalk Circle began in 1953 as Brecht finally settled on Dessau as the composer. After the premiere of this latest play in October 1954, he moved to Zeuthen in the suburb of Berlin. There he would live until his death.

The untimely death of Brecht in August 1956 also affected Dessau's career as he sought to find other lyricists who were compatible with his aesthetic views. Dessau now once again turned to the 12-tone system as his major vehicle, attracting young admirers in the avant-garde movement such as Luigi Nono, while he continued to put his ideas of music education in a socialist state into practice as he taught at the Zeuthener Grundschule. The result of the latter effort would be published in "Musikarbeit in der Schule". During the new phase, he also completed two operas which were based on Brecht's ideas. Puntila was premiered in 1966, and Einstein, 1974.

Paul Dessau died in Königs-Wusterhausen near Berlin on 28 June 1979.