Born 23 July 1886 in Glasgow, but educated in Manchester. Brown served an apprenticeship with the British Westinghouse Electric and Manufacturing Company (later Metropolitan-Vickers Electrical Company Ltd) at Trafford Park, Manchester.

In January 1915 he gained a commission in the Manchester regiment and took part in the second battle of Ypres before being transferred to the Royal Flying Corps and trained as an observer. In November 1915 he permanently injured one leg when he was shot down over Valenciennes in France. He remained a prisoner of war of the Germans until he was repatriated in September 1917. He then worked in the aircraft production department of the Ministry of Munitions until the end of the war.

In 1919 Brown, visited Vickers of Weybridge seeking a post, shortly after the firm had decided to make an attempt on the first direct flight across the Atlantic for the prize of £10,000 offered by the Daily Mail. Brown was offered the position of navigator, alongside John Alcock as pilot.

After the flight, Brown returned to work for Vickers Ltd and then again for Metropolitan-Vickers. During the Second World War he returned to the Royal Air Force in order to train pilots in navigation and engineering, though he never flew again after Alcock's death in 1919.

He died at his home in Swansea on 4 October 1948 from an accidental overdose of veronal. A memorial to Alcock and Whitten Brown was erected in 1952, near the field from which they took off at St John's, by the Historic Sites and Monuments Board of Canada. A memorial by William McMillan was erected at London Heathrow airport.