Baptised on 22 August 1734 at Denton in Lincolnshire. He was the only son of Colonel William Welby of Denton and his wife Catherine.
Educated at Eton School, before being admitted to Clare College as a Fellow Commoner in 1753 and then at the Middle Temple in 1756.
Member of Parliament for Grantham from 1802 to 1806. He also served as High Sheriff of Lincolnshire from 1796 to 1797.