Brown was the son of a Scottish Episcopalian clergyman. He studied medicine at the universities of Aberdeen and Edinburgh and spent five years in the British army serving in Ireland as an ensign and assistant surgeon (1795–1800). A visit to London in 1798 brought Brown to the notice of Sir Joseph Banks (Banks, Sir Joseph, Baronet), president of the Royal Society. Banks recommended Brown to the Admiralty for the post of naturalist aboard a ship (the Investigator) for a surveying voyage along the northern and southern coasts of Australia under the command of Matthew Flinders.

Brown sailed with the expedition in July 1801. The Investigator reached King George's Sound, Western Australia, an area of great floral richness and diversity, in December 1801. Until June 1803, and while the ship circumnavigated Australia, Brown made extensive plant collections. Returning to England in October 1805, Brown devoted his time to classifying the approximately 3,900 species he had gathered, almost all of which were new to science. The results of his Australian trip were partially published in 1810 as his Prodromus Florae Novae Hollandiae . . . , a classic of systematic botany and Brown's major work, in which he laid the foundations for Australian botany while refining the prevailing systems of plant classification. Disappointed by its small sale, however, he published only one volume. Brown's close observation of minute but significant details was also shown in his publication on Proteaceae, in which he demonstrated how the study of pollen-grain characters could assist in the classification of plants into new genera. In 1810 Banks appointed Brown as his librarian and in 1820 bequeathed him a life interest in his extensive botanical collection and library. Brown transferred them to the British Museum in 1827, when he became keeper of its newly formed botanical department.

In 1828 he published a pamphlet, A Brief Account of Microscopical Observations . . . , in which he recorded that, after having noticed moving particles suspended in the fluid within living pollen grains of Clarkia pulchella, he examined both living and dead pollen grains of many other plants and observed a similar motion in the particles of all fresh pollen. Brown's experiments with organic and inorganic substances, reduced to a fine powder and suspended in water, then revealed such motion to be a general property of matter in that state. This phenomenon has long been known as Brownian motion (q.v.). In 1831, while dealing with the fertilization of Orchidaceae and Asclepiadaceae, he noted the existence of a structure within the cells of orchids as well as many other plants that he termed the “nucleus” of the cell. These observations testify to the range and depth of his pioneering microscopical work and his ability to draw far-reaching conclusions from isolated data or selected structures. Brown was elected a fellow of the Royal Society in 1810.