Frederick's twin brother, Edward, was a military officer, colonial governor, and founder of Halifax, Nova Scotia.

His other brother, Charles Cornwallis, was the general of the American Revolutionary War.

Cornwallis was educated at Eton College, proceeding in 1760 to Christ Church, Oxford.

In 1774-75 he served as Master's Mate aboard HMS Pallas, which was under the command of his brother William and stationed off the west African coast.

While he was Bishop of Lichfield and Coventry he gave permission for the construction of a new Poorhouse (Workhouse) at Eagle House, Eccleshall.