Zambrowski was born into a Jewish family in Warsaw. He was a member of the Communist Party of Poland (1928–1938) and of the Central Committee of the Communist Association of Polish Youth (1930–1938). During World War II in the Soviet Union, he was one of the main organisers and leaders of the Union of Polish Patriots (ZPP) from 1943 and of the Central Bureau Communists of Poland (CBKP) in 1944. He was the head of the Political and Educational Leadership of the First Polish Army (1944–1945).
From 1944, Zambrowski was a member and one of the leaders of the Polish Workers' Party (PPR) and then, from 1948 to 1968, of the Polish United Workers' Party (PZPR). He was in the PZPR's Central Committee (1948–1964) and held the office of the secretary of the Central Committee (1948–1954 and 1956–1963). He was in the PZPR's Politburo from 1948 to 1963. In 1956, he was a leader of the faction in the PZPR known as Puławianie. Zambrowski was a deputy in the State National Council (1944–1947) and then in the Sejm (1947–1965), where he was Deputy-marshal of the Sejm (1947–1952). In 1945–1954, he was the chairman of a special commission for combating economically harmful activities and misconduct; in 1963–1968 vice-president of the Supreme Audit Office (NIK).
He is the father of journalist Antoni Zambrowski.
- Korboński, Stefan (1989). The Jews and the Poles in World War II. Hippocrene Books. ISBN 9780870525919.
- Jacobs, Jack (2017-03-24). Jews and Leftist Politics: Judaism, Israel, Antisemitism, and Gender. Cambridge University Press. ISBN 9781107047860.
- "Zambrowski Roman". WIEM Encyklopedia (in Polish). Retrieved 2007-10-08.