Willis was born in Hampstead, London, in 1889. He joined HMS Britannia as a naval cadet in 1904; subsequently serving on HMS Hindustan, Glory, Sprightly, Donegal, Good Hope and Vernon. He served during World War One on HMS Magnificent, Donegal, Fearless, Vernon, Saumarez and Wallace. Between 1918-19 he served in the Baltic in operations against the Bolsheviks. In 1920 he served on HMS Renown during the cruise of HRH the Prince of Wales to West Indies, Australia and New Zealand.

Between the wars he was promoted to Commander in 1921 and Captain in 1929 and served (successively) on HMS Vernon; at the Naval College, Greenwich; on HMS Coventry; the Tactical School at Portsmouth; on HMS Warwick; the Naval War College, Greenwich; on HMS Kent; on HMS Nelson; on HMS Vernon, the Torpedo School Portsmouth; and on HMS Barham.

In the period February 1939-April 1941 he was Chief of Staff to Commander-in-Chief Mediterranean (Admiral Sir Dudley Pound who was succeeded by Admiral Sir Andrew Cunningham in June 1939). In 1940-1 he took part in various Fleet operations in the Mediterranean, including the Battle of Calabria in July 1940, and the attack on Italian Fleet at Taranto in October 1940.

In August 1941 he was appointed Commander-in-Chief South Atlantic with acting rank of Vice-Admiral and responsible for convoys passing through this area to Middle East and for operations against enemy submarines and ocean raiders. In February 1942 he transferred to HMS Resolution as Vice-Admiral Commanding 3rd Battle Squadron and Second in command Eastern Fleet under Admiral Sir James Somerville, Commander-in-Chief. This Fleet was formed after the loss of HMS Prince of Wales and Repulse during the fall of Singapore and was assigned the task of protecting British territory and sea communications in the Indian Ocean.

In March 1943 he hoisted Flag in HMS Nelson as Flag Officer commanding Force "H", the force of Battleships, Aircraft Carriers and Destroyers which covered North African Operations and afterwards the invasion of Sicily and Italy (Salerno). In October 1943 he became Commander-in-Chief Levant after the Armistice with Italy (which was signed aboard his Flagship HMS Nelson at Malta) when Force "H" dispersed. As Commander-in-Chief Levant he conducted the Dodecanese operations of Autumn 1943 and attended the Cairo Conference of that year. He returned to the UK in 1944 and became Second Sea Lord (Chief of Naval Personnel) on the Board of Admiralty and held the appointment till February 1946. He was Appointed Commander-in-Chief Mediterranean in 1946 and Commander-in-Chief Portsmouth in 1948.

He was promoted to Rear-Admiral in 1940; Vice Admiral in 1943; Admiral in 1945 and Admiral of the Fleet in 1949. He was created CB in 1940, KBE in 1945 and GCB in 1946. He died in April 1976.