He studied medicine at Cambridge University and was also a student at Leyden in the Netherlands. He graduated Doctor of Medicine and became a Fellow of the Royal Society in 1732.
Fuller went to Jamaica before 1735, where he took over the family estate from his father. He was elected to the Assembly in 1735 and called to the council in 1737. He was made a judge of the supreme courts but as a result of disputes with the governor Edward Trelawny he was removed from the council and the bench and returned to England in 1749.
He was back in Jamaica in around 1752 and was appointed Chief Justice by the next governor Charles Knowles.
On 26 April 1737 Fuller married Ithamar Mill, daughter of Richard Mill of Jamaica. She died in Jamaica on 22 April 1738 at the age of seventeen.
He died on 7 May 1777, and was buried at Waldron, Sussex, on 15 May 1777.
Royal Society; 12th Parliament of Great Britain. 13th Parliament of Great Britain]
Fuller was a Member of Parliament for New Romney from 1756 to 1761, for Maidstone from 1761 to 1768, and for Rye from 1768 to 1777.