Arthur was the son of Arthur Charles Wellesley, 4th Duke of Wellington and Kathleen Bulkeley Williams. He attended Eton between 1890 and 1895. He then attended Trinity College at Cambridge.

He joined the Grenadier Guards and fought in the Boer War in 1900, and later in World War I. In 1934 he succeeded to the Dukedom; he was also a Justice of the Peace.

The Duke was a supporter of several far right-wing causes. He was a member of the Anglo-German Fellowship from 1935 and served as President of the Liberty Restoration League, which was described by Inspector Pavey (an ex-Scotland Yard detective employed by the Board of Deputies of British Jews to infiltrate the far right) as being anti-semitic. When Archibald Maule Ramsay formed the 'Right Club' in 1939, Wellington chaired its early meetings.