Banks was schooled at Harrow School and Eton College before attending Christ Church College, Oxford, from 1760 to 1763; he inherited a considerable fortune from his father in 1761. Banks then traveled extensively, collecting plant and natural history specimens in journeys to Newfoundland and Labrador (1766), around the world with Captain James Cook (Cook, James) (1768–71), and to Iceland (1772).

Banks was interested in economic plants and their introduction into countries. He was the first to suggest (1805) the identity of the wheat rust and barberry fungus, and he was the first to show that marsupial mammals were more primitive than placental mammals. In his capacity as honorary director of the Royal Botanic Gardens at Kew (Kew Gardens) (near London), he sent many botanical collectors to various countries. His house became a meeting place for the exchange of ideas. After he became president of the Royal Society (1778–1820), he improved the position of science in Britain and cultivated interchange with scientists of other nations; he was, however, accused by many fellow scientists of exercising excessive authority as president and even of being “despotic.” In 1781 he was made a baronet. The order of Knight Commander of the Bath was bestowed upon him in 1795, and two years later he was admitted to the Privy Council.

Banks's herbarium, considered one of the most important in existence, and his library, a major collection of works on natural history, are now at the British Museum. Banks' Florilegium, a collection of engravings of plants compiled by Banks and based on drawings by Swedish botanist Daniel Solander during Cook's 1768–71 voyage, was not published in full until 1989.