Goldenbaum was born in Parchim. During World War I he served in the military and he participated in the German November Revolution. In 1919 he joined the left-wing USPD and a few years later the Communist Party of Germany.
From 1923 to 1925 he was a member of the city council of Parchim and from 1924 to 1932 he was a member of the Landtag of Mecklenburg-Schwerin. From 1932 to 1933 he was the editor of Volkswacht, a communist newspaper. After the Nazis seized power he became a farmer and a member of the German resistance.
In 1944 he was arrested and he spent the last year of the war in concentration camp Neuengamme. In 1945, he was one of very few who survived the sinking of the SS Cap Acrona which claimed over 4000 lives.
After the war he joined the Socialist Unity Party (SED), but in 1948 he co-founded the communist-sponsored Democratic Farmers' Party of Germany (DBD). The DBD was a close ally of the SED. Until 1982, Goldenbaum was the Chairman of the party.
From 1949 to 1990 Goldenbaum was a member of the People's Chamber. From 1949 to 1950 Goldenbaum was East Germany's first Minister of Agriculture and Forestry. Goldenbaum supported the SED's collectivisation in the 1950s and 1960s. From 1950 to 1963 he was the deputy chairman of the People's Chamber. After 1963 he was a member of the Presidium of the People's Chamber.