Solomon or Salomo Birnbaum was the oldest of the three sons of Jewish philosopher Nathan Birnbaum and his wife Rosa Korngut. His younger brother Uriel Birnbaum grew up to be an artist and poet. Salomo served in the Austro-Hungarian Army in World War I, and then attended and earned a doctorate from the University of Würzburg, Germany. From 1922 to 1933, he held the first chair in Yiddish at the University of Hamburg. After the rise of Nazism, Salomo Birnbaum and his wife Irene Gruenwald and their children fled to Britain. From 1936 to 1957, he was a lecturer on Hebrew paleography and epigraphy at the School of Oriental and African Studies at the University of London. Beginning in 1938, he also taught Yiddish in the School of Slavonic and East European Studies. During World War II, he worked in the postal censorship bureau for the British authorities. In 1970, he emigrated to Canada, settling in Toronto. He acquired a large archive of his father's works.