Stephenson joined the army, serving in the 9th Regiment of Light Dragoons and the 3rd Dragoon Guards. He saw action at the Battle of Famars and the Siege of Valenciennes in 1793, and in later skirmishes was seriously wounded.[1]
In 1803, he was appointed Deputy Judge Advocate of the South West District, and later served on a commission on military expenditure. In 1812 he was appointed Master of the King's Household at Windsor, and in 1823 was appointed to superintend the finances of Prince Frederick, Duke of York and Albany.[1]
Stephenson succeeded Sir James Wyatt as Surveyor-General of the Board of Works in 1813. As Surveyor-General, in 1829, he commissioned Sir John Soane to design the New State Paper Office in Duke Street, east of London's St James's Park, as a purpose-built repository for national records in England (superseded in 1856 by Sir James Pennethorne's Public Record Office in Chancery Lane, and demolished in 1862).[2] When the Board merged with the Department of Woods and Forests in 1832, Stephenson was appointed a Commissioner in that department.
Promoted a Knight Commander of the Guelphic Order of Hanover in 1830 and Knight Grand Cross in 1834, he died at his London home in Bolton Row, Piccadilly on 10 June 1839 and was buried in the family vault in Kensington churchyard on 15 June.[1]