Cunningham was born in Dublin, Ireland. He was educated at Cheltenham College and the Royal Military Academy before taking a commission in the army in 1906. During World War I, he served with the Royal Horse Artillery, and was awarded a Military Cross in 1915 and the DSO in 1918. For two years after the war he served in the Straits Settlements.

In 1937 Cunningham became the Commander Royal Artillery of the 1st Infantry Division. This was followed in 1938 by promotion to major-general and appointment as commander of the 5th Anti-Aircraft Division.

After the beginning of World War II, Cunningham held a number of short appointments commanding infantry divisions in the United Kingdom (including 66th Division) before being promoted to lieutenant-general to take command of the British East Africa Forces in Kenya. During the East African Campaign General Archibald Wavell the Commander-in-Chief of the British Middle East Command directed Cunningham to retake British Somaliland and free Addis Ababa, Ethiopia, from the Italians whilst forces under the command of Lieutenant-General Sir William Platt would attack from Sudan in the north through Eritrea. Cunningham's offensive started with the occupation of the Indian Ocean ports of Kismayu (Italian: Chisimaio) and Mogadishu (Italian: Mogadiscio), the Italians having fled into the interior of Somalia. On 6 April 1941, Cunningham's forces entered Addis Ababa. On 11 May the northernmost units of Cunningham's forces, under South African Brigadier Dan Pienaar linked with Platt's forces under Major-General Mosley Mayne to besiege Amba Alagi. On 20 May, Mayne took the surrender of the Italian Army, led by Amedeo di Savoia, 3rd Duke of Aosta, at Amba Alagi. Cunningham's campaign was a swift action which resulted in the taking of 50,000 prisoners and the loss of only 500 of his men.

His success in East Africa led to Cunningham's appointment to command the newly-formed 8th Army in North Africa in August 1941. His immediate task was to lead General Sir Claude Auchinleck's Libyan Desert offensive which began on 18 November. However, early losses led Cunningham to recommend the offensive be curtailed. This advice was not accepted by his superiors, and Auchinleck relieved him of his command. He returned to Britain to serve the remainder of the war as Commandant of the Staff College (1942) and General Officer C-in-C in Northern Ireland (1943) and Eastern Command (1944). He was knighted in 1941.

After World War II, Cunningham, who was promoted to general on 30 October 1945, returned to the Middle East as High Commissioner of Palestine; he served in the position from 1945 to 1948 when the British mandate in Palestine expired and Israel was proclaimed an independent state. He had retired from the army a little less than two years before this in October 1946 when he relinquished the role of Commander-in-Chief Palestine. He also served as Colonel Commandant of the Royal Artillery until 1954.

Cunningham died in Royal Tunbridge Wells, Kent, England.