He was the third son of the George Venables-Vernon, 1st Baron Vernon (1710-1780), and took the additional name of Harcourt on succeeding to the property of his cousin, the last Earl Harcourt, in 1831.
On 18 August 1791 he was nominated Bishop of Carlisle in succession to Dr. John Douglas, and was consecrated on 6 November following. For sixteen years he administered the affairs of the see of Carlisle with good sense and discretion, spending more than the whole income of the see upon the wants of his diocese.
Harcourt was a member of the queen's council who had charge of George III during his illness. He was an eloquent speaker, and occasionally spoke in the House of Lords on ecclesiastical matters, but usually abstained from political contentions. He lived under five successive monarchs, and was respected for benevolence and simplicity of character. On 15 January 1831 he took the surname of Harcourt only on inheriting the large estates of the Harcourt family, which came to him on the death of his cousin, Field-marshal William, third and last Earl Harcourt.
In 1835 he was appointed one of the first members of the ecclesiastical commission. In 1838 he was offered the renewal of the Harcourt peerage, but declined it, not wishing to be fettered in his parliamentary votes. York Minster was twice burnt down during his primacy, 1829 and 1841, and he contributed largely to both restorations. Archbishop Harcourt preached his valedictory sermon in York Minster on 13 November 1838. However Harcourt continued to enjoy good health, and as late as 1 November 1847 visited York and inspected the repairs of the chapterhouse. He died at the palace, Bishopthorpe, near York, on 5 November 1847, and was buried at Stanton Harcourt, Oxfordshire, 13 Nov
His second son, the Rev. Levesox Vernon Harcourt, was chancellor of York and the author of The Doctrine of the Deluge,, and of other theological works. His fourth son was William Vernon Harcourt, the founder of the British Association for the Advancement of Science. His eighth son was Admiral Octavius Henry Cyril Harcourt whilst his youngest daughter, Georgiana, distinguished herself as a translator.