Son of Rev. Dr. Alexander Webster, and Mary Erskine. A maternal cousin of James Boswell. Webster married Charlotte Kerr (d. 1804) in 1771.1, with whom he had two children, Alexander (b. 1778) and Eleonora (b. 1780). Webster was a Captain in the 4th Foot Regiment until he retired from the army in 1777.2
Boswell went with Webster to Arniston on October 28, 1762.