Plant collector. Born in Traquair in the Scottish Borders, the son of a nurseryman, Dickson began his own nursery in Perth before moving to London to work in nurseries at Kensington and Hammersmith. In 1772, he started his own plant and seed shop in Covent Garden and became acquainted with horticulturist William Forsyth (1737 - 1804), whom he supplied with plants. With particularly interests in mosses and other non-flowering plants, Dickson made several plant-hunting expeditions around Scotland, including to the Hebrides. Dickson published a four-volume treatise on cryptogams, Fasciculus Plantarum Cryptogamicarum Britanniae (1785 - 1801), which described 400 species, many of which had not been identified previously in Britain.
He was also friendly with Joseph Banks, who gave Dickson access to his botanical library and employed him to tend the garden of the British Museum. In 1786, his first wife died, Dickson married the sister of explorer Mungo Park (1771 - 1806). He introduced Park to Banks, who sponsored Park's expedition to West Africa in 1795.
Dickson was a founder of the Linnean Society in 1788 and of the Royal Horticultural Society in 1804.
He retired to Croydon, a wealthy man. A genus of tree-ferns is named Dicksonia in his honour.