Webb was born in Wethersfield, Connecticut, a descendant of Richard Webb of Gloucestershire, England, who settled in Boston in 1632 and moved to Hartford, Connecticut, in 1635. He fought in the Revolutionary War, rising to the rank of brigadier general. He was one of the original thirteen officers who met at the Verplanck House in Fishkill, New York, in 1783 to form the Society of the Cincinnati, and when Washington was inaugurated president, Samuel Webb was the grand marshal of the proceedings.