In 1742, he matriculated at St Mary Hall, Oxford but did not graduate. During 1747–1748, he travelled in Continental Europe, principally Holland, Germany and Switzerland. On November 19 1748 he succeeded his father. From 1748–1768 he was Member of Parliament for St Germans, Cornwall, the place of his family estate Port Eliot. In succession, he became Member of Parliament (MP) for Liskeard (1768–1774), for St Germans (1774–1775), and for Cornwall (1775–1784).
In 1751, Edward was appointed Receiver General of the Duchy of Cornwall. From 1760 until 1776, Edward was one of the eight Commissioners of Trade and Plantations, and in 1775 he again became Receiver General of the Duchy. However, in 1776 he notably voted against the employment of Hessian Troops, and resigned from the Board of Trade and Plantations, and from the government.
On January 13 1784 he was formally created 1st Baron Eliot of St Germans, and he took his seat in the House of Lords on February 2 1784. In 1789 he changed his surname from Eliot to Craggs-Eliot, presumably to prevent the extinction of the Craggs surname. However, his children generally used the surname Eliot.
Edward was an acquaintance of Dr Samuel Johnson and a patron of Sir Joshua Reynolds.
Edward married on September 25 1756 to Catherine Elliston (September 1735 – February 23 1804), daughter of Captain Edward Elliston and Catherine Gibbon, the aunt of Edward Gibbon. Edward and Catherine had four children:
Edward died at his Port Eliot estate on February 17 1804, and was buried at St Germans, Cornwall