Plant-hunter. Born in Penicuik, the son of a weaver, he trained at the Botanic Garden on Leith Walk and then worked for the Duke of Northumberland in London. Then, while working for George Hibbert, a well known garden-owner and nurseryman in London, he was sent to the Cape Colony in South Africa to collect plants (1798 - 1803). During this trip he worked with another Scottish plant hunter, William Roxburgh (1751 - 1815), who was collecting on behalf of Calcutta Botanic Garden. Niven returned to the Cape in 1802-12. He returned to Penicuik, marrying and starting a business. He is buried in the parish churchyard there.
His collection of dried plants is held by the National Botanic Gardens of Ireland in Dublin. The genus Nivenia and the species Erica nivenia, Serruria nivenii and Gladiolus nivenii were all named after him.