Hely-Hutchinson is born on May 15, 1757, the son of John Hely-Hutchinson and the Christiana Hely-Hutchinson, 1st Baroness Donoughmore. He is educated at Eton College, Magdalen College, Oxford, and Trinity College, Dublin.
Hely-Hutchinson enters the Army as a cornet in the 18th Royal Hussars in 1774, rising to a lieutenant the following year. In 1776 he is promoted to become a captain in the 67th (South Hampshire) Regiment of Foot, and a major there in 1781. He moves regiments again in 1783, becoming a lieutenant-colonel in, and colonel-commandant of, the 77th Regiment of Foot, which is, however, disbanded shortly afterwards following an earlier mutiny. He spends the next 11 years on half-pay, studying military tactics in France before serving as a volunteer in the Flanders campaigns of 1793 as aide-de-camp to Sir Ralph Abercromby.
In March 1794 Hely-Hutchinson obtains brevet promotion to colonel and the colonelcy of the old 94th Regiment of Foot and then becomes a major-general in May 1796, serving in Ireland during the Irish Rebellion of 1798, where he is second-in-command at the Battle of Castlebar under General Gerard Lake. In 1799, he is in the expedition to the Netherlands.
Hely-Hutchinson is second-in-command of the 1801 expedition to Egypt, under Abercromby. Following Abercromby’s death in March after being wounded at the Battle of Alexandria, he takes command of the force. From then he is able to besiege the French firstly at Cairo which capitulates in June and then besieges and takes Alexandria, culminating in the capitulation of over 22,000 French soldiers. In reward for his successes there, the Ottoman Sultan Selim III makes him a Knight, 1st Class, of the Order of the Crescent.
On December 18, 1801 Hely-Hutchinson is created Baron Hutchinson in the Peerage of the United Kingdom, gaining a seat in the House of Lords. In recognition of his “eminent services” during the “late glorious and successful campaign in Egypt,” at the request of the King, the Parliament of the United Kingdom settles on Lord Hutchinson and the next two succeeding heirs male of his body an annuity of £2000 per annum, paid out of the Consolidated Fund.
Hely-Hutchinson is promoted lieutenant-general in September 1803, and made a full general in June 1813. In 1806, he becomes colonel of the 57th (West Middlesex) Regiment of Foot, transferring in 1811 to be colonel of the 18th Regiment of Foot, a position he holds until his death. He also holds the position of Governor of Stirling Castle from 1806 until his death.
Hely-Hutchinson sits as Member of Parliament (MP) for Lanesborough from 1776 to 1783 and for Taghmon from 1789 to 1790. Subsequently, he represents Cork City in the Irish House of Commons until the Act of Union 1800 and is then member for Cork City in the after-Union Parliament of the United Kingdom until 1802.
Hely-Hutchinson dies on June 29, 1832, never having married.