He was born in Glasgow, the son of John Moore, a doctor and writer. A career soldier he joined the British Army in 1776, an ensign in the 51st Foot then based on Minorca. He first saw action in 1778 during the American Revolutionary War under the [[Douglas Hamilton, 8th Duke of Hamilton|8th Duke of Hamilton]]. In 1783 he returned to Britain and in 1784 he was elected to Parliament for Lanark, Selkirk, Peebles and Linlithgow.
In 1787 he was made a Major and joined the 60th briefly before returning to the 51st. In 1791 his unit was assigned to the Mediterranean and he was involved in campaigning in Corsica and was wounded at Calvi. He was given a Colonelcy and became Adjutant-General to Sir Charles Stuart. Personal problems in Corsica led to him being reassigned to Sir Ralph Abercromby in the West Indies. In 1798 he was made a Major-General and served in Ireland.
In 1799 he commanded a brigade in the expedition to Egmont-op-Zee, his force was badly defeated and he was seriously injured himself. He recovered to lead the 52nd regiment during their campaigns in Egypt. He returned to England in 1803 to head the training of the army at Shorncliffe camp. In 1804 Moore was knighted and promoted to Lieutenant-General. In 1806 he returned to active duty in the Mediterranean and then in 1808 in the Baltic to assist the Swedish. Disagreements with Gustavus IV led to him being soon sent home where he was ordered to Portugal.
Moore took comand of the British forces in the Iberian penninsular following the return of more senior commanders to Britain to face an inquiry over the Convention of Cintra. When Napoleon arrived in Spain with 200,000 men Moore was forced to retreat northwards over winter to La Coruņa. The British forces rallied to hold the town while they were evacuated and Moore was killed during the Battle of Coruņa (sometimes called Corunna) and was buried in the ramparts of the town. When the French took the town a monument was built over his grave by the orders of Soult. The monument was rebuilt and made more permanent in 1811.