Homburg arrived in South Australia in the year 1857. He was employed in a land agency business until 1868, when he was articled to James Boucaut. The last two years of his articles were served in the office of Sir John Downer, and he was admitted to the bar in April 1874.
Homburg was elected to the South Australian House of Assembly as a representative for Gumeracha in April 1884, and at the election of 1887 was re-elected with the Sir Robert Dalrymple Ross. In April 1890 he was again returned with Theodore Hack. In 1880 for a short period he was president of the German Club. He was appointed Attorney-General in Thomas Playford's second Ministry in August 1890, and held office till June 1892, when he retired with his colleagues. Homburg was again Attorney-General from 15 October 1892 to 16 June 1893 and from 4 July 1904 to 24 February 1905 (also being Minister of Education in the latter term). Homburg held the seat of Gumeracha until its abolition on 2 May 1902. From 3 May 1902 to 26 May 1905 Homburg represented the Assembly for Murray.
Homburg was appointed a justice of the Supreme Court of South Australia in 1905. He died in Medindie, Adelaide on 23 March 1912; he was survived by a total of four sons and four daughters from his two marriages.
- Harmstorf, Ian. "Homburg, Robert (1848–1912)". Australian Dictionary of Biography. Canberra: Australian National University.
- Mennell, Philip (1892). " Homburg, Robert". The Dictionary of Australasian Biography. London: Hutchinson & Co. Wikisource
- "Hon Robert Homburg Snr". Former Member of Parliament Details. Parliament of South Australia.