He was born Henry Crabb, the son of Hester Crabb, a London widow. He inherited in 1746 the properties of her cousin Richard Boulton, an East India director from 1718 to 1738 whose surname he adopted in addition to his own.
In early life he worked as a clerk in the East India Company's offices in London as paymaster and as clerk to the Shipping Committee (1737 to 1757). In 1753 he was elected a Director of the East India Company for the first time, holding the position for the conventional 3 years. He was afterwards re-elected in 1758, 1763, 1767 and 1772. In 1764 he served as Deputy Chairman and was Chairman the following year and again in 1768 and 1773. From 1755 he was described as a merchant. 
He died unmarried.
- "The Directors of the East India Company, ..1754-1790" (PDF). James Gordon Parker. Retrieved 8 December 2017.
- "CRABB BOULTON, Henry (c.1709-73), of Crosby Sq., Bishopsgate, and Thorncroft, nr. Leatherhead, Surr". History of Parliament Online. Retrieved 8 December 2017.
|Parliament of Great Britain|
| Member of Parliament for Worcester
With: Thomas Vernon 1754–1761
John Walsh 1761–1773
Thomas Bates Rous