Clements Robert Markham was born on 20 July 1830 at Stillingfleet, Yorkshire, where his father was vicar. He was educated at Cheam and Westminster School. He was offered a cadetship in the Royal Navy through family connections, and in June 1844 joined Admiral Seymour's flagship HMS Collingwood for a four year voyage through the Pacific. This voyage enabled him to learn Spanish. He decided, though, that he would prefer to be an explorer rather than a naval officer. However, he stayed in the navy for a brief period in the Mediterranean. Early in 1850 he volunteered for an expedition to search for Franklyn's lost expedition to discover the Northwest Passage, returning to England in October 1851. He decided to leave the Royal Navy taking issue with the amount of idleness that occupied long periods of his service along with his distaste for corporal punishment. He left the Royal Navy at the end of 1851.

His initial exploration expeditions were to Peru (1852-3 and 1859-60) and India (1861). He was employed as a junior clerk in the Inland Revenue and then the India Office, which allowed him time off to travel. In 1867 he became head of the India Office's geographical department and was attached to Sir Robert Napier's HQ for the military expedition to Abyssinia in 1867-8, for which service he was awarded the CB. He returned to the Arctic in 1875-6.

He was elected to the Royal Geographical Society in 1854 and in 1863 he was appointed honorary secretary, a position he held for 25 years. He was also secretary of the Hakluyt Society until 1886, subsequently being president until 1910, and translating 22 volumes from Spanish into English. In 1873 he was elected a Fellow of the Royal Society. In 1888 he resigned as Hon. Secretary of the RGS, but in 1893 he was elected President, as a result of a dispute over women members. Also in 1893 he was promoted to KCB. Markham devoted his time to supporting Antarctic exploration, organising the funding of the Scott expedition of 1901-4, and consistently supporting Scott rather than Shackleton. He died on 30 January 1916 overcome by smoke when he set fire to his bedclothes while reading by candlelight.