He was the second son of Peter Hay of Megginch and Margaret, daughter of Patrick Ogilvy of Inchmartin. No date is recorded for his birth, but he was baptised 4 December 1570. Around 1588, Hay entered Scottish College at Douai, where he studied under his uncle Edmund Hay until 1596. He was initially introduced to court by his cousin the Earl of Carlisle. Hay served as a Gentleman of the Bedchamber from 1596. On 18 February 1598, he was granted the Carthusian priory of Perth and a seat in Parliament, but, finding the rents too low to live on, he returned the peerage. On 15 November 1600, he was given land for his services to the King on the occasion of the Gowrie conspiracy. He was knighted sometime before 18 October 1607, when he first appeared in the records as Sir George Hay. He was appointed Lord Clerk Register and a member of the Privy Council on 26 March 1616. He was instrumental in the passage of the Five Articles of Perth in 1618. In 1619 the Privy Council of Scotland wrote to King James to defend Hay's interest in glass and iron manufacture in Scotland, arguing that Scottish glass should be sold in England without custom duties. On 9 July 1622, he was appointed Lord Chancellor and Keeper of the Great Seal. On 19 July 1625, the lands of the Earldom of Orkney were transferred to him. On 7 May 1625, he was at the funeral of James VI and I in London, and was sworn in as a member of the Scottish Privy Council of Charles I. He was created Viscount of Dupplin and Lord Hay of Kinfauns on 4 May 1627; on 25 May 1633, he was created the Earl of Kinnoull on the occasion of the King Charles' coronation in Scotland. He resisted the king's regulations for lords of session, and upheld precedency over archbishop of St Andrews. In 1626, he began to suffer from old age. It was noted that he was absent from the Council in July 1626 as he was suffering from "the pain of the gute" very severely. Two years later his "known infirmitie and seekenesse" was noted. He died of apoplexy in London and was buried in St. Constantine's Church in Kinnoull, where a monument was erected in his honour.
