The seventh son of Charles Cornwallis, 4th Baron Cornwallis, he was educated at Eton College (1725-1728) and Christ's College, Cambridge (1732-1737), where he graduated with a BA. He was ordained a priest in 1742, and became a Doctor of Divinity in 1748.
Cornwallis was able to ascend quickly in the Church thanks to his aristocratic connections, and in 1746 was made chaplain to King George II and a canon of Windsor. In 1750 he became a canon at St Paul's Cathedral, and later that same year became Bishop of Lichfield and Coventry thanks to the patronage of the Duke of Newcastle, then Secretary of State.
On the death of Thomas Secker in 1768, his friendship with the then-prime minister, the Duke of Grafton, resulted in his appointment as Archbishop of Canterbury. As archbishop, his sociability and geniality made him popular. He was a consistent supporter of the administration of Lord North, and led efforts in support of dispossessed Anglican clergy in the American colonies during the American Revolution.
On the whole, Cornwallis has generally been judged as a competent administrator, but an uninspiring leader of the eighteenth century church - a typical product of eighteenth century latitudinarianism, whose lack of zeal paved the way for the differing responses of both the Evangelicals and the Oxford Movement in the early 19th century.
Frederick's twin brother was Edward Cornwallis, the "Founder of Halifax". His nephew was Charles Cornwallis, 1st Marquess Cornwallis, a British general during the American Revolution, and later Governor-General of India.