Born in St James's Square, London, William Henry Vane was the son of Henry Vane, 2nd Earl of Darlington, and Margaret Lowther, sister of James Lowther, 1st Earl of Lonsdale, and first styled Lord Barnard. He succeeded as third Earl of Darlington in 1792, was created Marquess of Cleveland in 1827, and Baron Raby and first Duke of Cleveland of the second creation in 1833. His grandmother, Grace, was a daughter of Charles Fitzroy, 1st Duke of Southampton and Cleveland.

After attending Christ Church, Oxford, he represented the boroughs of Totnes and Winchelsea in the House of Commons from 1788 until his elevation to the peerage. In 1792 he became colonel of the Durham militia, in 1793 lord lieutenant of Durham and in 1794 colonel commandant of the Durham cavalry. In 1787 he married Katherine Margaret Powlett, daughter of the 6th Duke of Bolton, and in 1813 Elizabeth, daughter of Robert Russell of Newton, Yorkshire.

A well-known and respected sportsman he retained his great love for foxhunting all his life. He spent much of his time each year at Raby Castle in Durham, near the Yorkshire border, where he first hunted his father's hounds. He maintained two packs which he hunted on alternate days.

He entered racing in 1791 and at Raby he also established his large stud of racing horses and broodmares. A patron of the turf for the next fifty years he bred and owned numerous very good horses. His stable was sometimes called the "terror of the north". His home bred Chorister (b c 1828 Lottery) won the St Leger Stakes in 1831. Aside from those horses noted on the left, he also owned the St Leger and Ascot Gold Cup winner Memnon (b c 1822 Whisker) and the stallion Trustee (ch c 1829 Catton).

He died in St James's Square on January 29, 1842, and was buried in Staindrop church.