[1] Smyth was the son of John Smyth of Heath Hall, Heath, West Yorkshire and his wife Bridget Foxley, daughter of Benjamin Foxley of London.
He was educated at Westminster School and was admitted at Trinity College, Cambridge in 1766.
He was Master of the Mint from 1802 to 1804, and a Commissioner of the Board of Trade in 1805.
[4] In 1778, Smyth married Lady Georgiana FitzRoy, eldest daughter of Augustus Henry FitzRoy, 3rd Duke of Grafton.
[4] Their son Smyth died 12 February 1811 in London.