Robert Cullen was the son of the noted Edinburgh physician, chemist and professor, William Cullen. He married Mary Russell (d.1818) but had no children.1
Cullen was educated at Edinburgh University and admitted to the Faculty of Advocates in 1764. He later became a judge, serving as one of the senators of the College of Justice (1796-9) and as a Lord of Justiciary (1799-1810).
In 1783, he co-founded, with his father and other prominent Edinburgh citizens, the Royal Society of Edinburgh.
- 1In 1813, Cullen's widow, Mary, married J. J. Alexander, Esq. of St. Lucia, and died on that island in 1818.
Cullen was one of Boswell's professional colleagues. On August 16, 1773, Cullen came to meet and dine with Dr Johnson at Boswell's Edinburgh home together with the Duchess of Douglas, Sir Adolphus Oughton, Lord Chief Baron Ord, Sir William Forbes and Principal William Robertson.
Cullen stayed for supper, and they were joined by his father, the noted physician William Cullen, the philosopher Adam Fergusson and Boswell's close associate and fellow advocate Andrew Crosbie.