Reverend Henry Fulton was born in England in 1761. He enrolled in Trinity College, Dublin in 1788 where he received a Bachelor of Arts in 1792 and was ordained to the ministry of the established Church of Ireland by Bishop Barnard of Killaloe. He was sentenced to transportation to new South Wales for his part in the Irish Rebellion of 1798 and arrived aboard the 'Minerva' on 11th January 1800. He received a conditional pardon on 8th November 1800 and was sent to the Hawkesbury. In February 1801 he was sent to Norfolk Island where he remained until 1806, receiving  a full pardon in 1805 because of his work there. On his return to Port Jackson he was appointed acting Chaplain of Parramatta, Samuel Marsden being on leave of absence in England. He was officially suspended in 1808 because of his loyalty to the disposed Governor Bligh and reinstated as assistant Chaplin to the Colony in January 1810 by Governor Macquarie. He travelled to England with Bligh to testify at Leut-Colonel Johnston's court martial, returning on board the 'Mary' in May 1812.

He was made resident chaplain of Castlereagh and Richmond on 18th June 1814 and opened a seminary at his new parsonage at Castlereagh on 11th July 1814 where he instructed young gentlemen in the classics, modern languages and "such Parts of the  Mathematics, both in Theory and Practice, as may suit the taste of the Scholar".

The Poet, Charles Thompson junior, was among his students at Castlereagh. Thompson dedicated Wild Notes, from the Lyre of a Native Minstrel to Fulton when it was published in 1826.

The town of Castlereagh failed to flourish and Fulton's designation changed from "Chaplain of Castlereagh" to "Minister of the Parish of Penrith" in 1838.

He died on 17th November 1840, living four years after his wife, Ann,  and is buried in the vault of his son-in-law. John MacHenry, at the Castlereagh Cemetery.