Eliot was born in Cornwall, the son of Catherine, daughter and heir of Edward Elliston of Gestingthorpe, Essex, an East India Company captain, and Edward Craggs-Eliot, politician, created Baron Eliot in 1784. He went to Pembroke College, Cambridge in 1775, becoming friends with the futurePrime Minister, William Pitt the Younger, and graduated with an MA in 1780. He was elected Member of Parliament for St Germans, Cornwall from 1780 and for Liskeard from 1784. He soon became a Treasury minister from 1782, and was a member of the government of the Younger Pitt from 1783, being appointed King's Remembrancer in the Exchequer of pleas in 1785. In 1785 he married Harriot Pitt, the younger daughter of William Pitt the Elder and sister to the Younger Pitt. One year later, and five days after the birth of their only child, a daughter named Harriot Hester, Eliot's wife died as a result of complication from childbirth. Eliot never recovered from the grief of losing his wife. After Harriot's death, Eliot moved to Broomfield, near Clapham, where he came into contact with the Clapham Sect of evangelical reformers, whose cause he espoused. He had been a friend of William Wilberforce for some years, and the pair of them had accompanied Pitt to France. Now he found himself living close to Wilberforce and other leading members of the group dubbed ‘the Saints’. He began to take an active part in their reforming causes, including the abolition of the slave trade, prison reform and poor relief, the Proclamation Society, and Bishop Porteus’ Sunday Observance bill. He was active in lobbying the cause of the Clapham Sect in parliament and acted as a mediator between Wilberforce and Pitt in their campaigns. In 1793, having resigned from the Treasury on health grounds, Eliot was appointed joint commissioner for Indian affairs. He became an investor in the British East India Company stock, and was expected to become governor-general of Bengal. However, he suffered from a recurring chronic stomach disorder which made it impossible for him to take up that office. Eliot died at Port Eliot, Cornwall on 17 September 1797, and was buried at St Germans on 26 September 1797. He had remained close to Pitt and Wilberforce, who both lamented his passing. His brother John succeeded to the barony and in 1815 was created Earl of St Germans.