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.
- 1. In 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.