Born in Gladwyne, Pennsylvania into a military family he entered West Point in 1903, aged only seventeen. At the institution he joined and later led the student "Black Hand". He wanted to join the cavalry but his poor discipline and average academic achievements resulted in him being commissioned in 1907 as a Second Lieutenant in the infantry, initially assigned to the newly-won Philippines.
In 1909 while stationed at Fort Jay he was offered the chance of flight instruction. In 1911 he began the course with fellow soldier Thomas DeWitt Milling at Simms Station, the Wright brothers' school. After around four hours of lessons over two months he took his first solo flight in May and received his civil certificate in July, his military rating was awarded a year later, the first man to qualify.
The first two Army pilots then became instructors, flying for the Aviation Section of the Signal Corps out of College Park, Maryland or Barnes Farm, Georgia. Arnold set an altitude record of 6,540 feet in June and had his first serious crash in July and in September there was the first death, of Corporal Frank Scott, another pilot died later that month. In October Arnold won the inaugural Mackay Trophy for "the most outstanding military flight of the year". In September Arnold took a ground job as assistant in the Office of the Chief Signal Officer.
In 1913 he married Eleanor Pool and lost his flying status, only unmarried pilots were allowed. Reassigned to the Philippines he first met George Catlett Marshall, soon to become his friend and long-time supporter. In 1915 with war imminent Arnold was re-assigned to the Aviation Section at Rockwell Field and promoted to captain. He had to requalify for flying, he completed the course in November 1916 and was promoted to Captain. Briefly assigned to the Panama Canal Zone as a squadron commander he was recalled to Washington just before April 1917. He was assigned as an executive officer of the Air Division and given a temporary colonelcy. He never saw combat in WW I, he only just made it to Europe before the armistice, given orders to France in October 1918 he fell ill with influenza and did not arrive until November when poor weather prevented any operations before the end.
The improvements in aircraft during the war and the creation of bodies such as the National Advisory Committee for Aeronautics greatly improved the potential for US Army airpower. Arnold was ordered back to Rockwell Field in 1919 as district supervisor and Major, overseeing demobilization but working hard to preserve and promote aviation with shows and publicity stunts. At Rockwell Field Arnold first established relationships with the men that would be his main aides, Carl Spaatz and Ira Eaker, while supporting at a distance the highly visible efforts of William L. Mitchell. In 1924 Arnold was recalled to Washington to join the staff of the chief of the Air Service, General Mason Patrick. Arnold also attended the Army Industrial College at this time. When Mitchell was court-martialled in 1926 Arnold was also threatened, in 1927 he was sent to Fort Riley, Kansas - a dingy cavalry post and as far from aviation as could be.
Arnold took his punishment and after his tour at Fort Riley he attended the Army Staff College before returning to Army aviation at Fairfield Air Service Depot, Ohio in late 1928. In 1930 he was moved to Wright field to join the staff of General Pratt and in late 1931 he took command at March Field, California of the 1st Wing as a Lieutenant-Colonel, his first promotion in over ten years. In 1934 he won his second Mackay Trophy, leading ten of the new B-10 bombers 18,000 miles from Washington to Fairbanks, he was also promoted to temporary Brigadier-General.
In 1936 Arnold returned to Washington as Assistant Chief of the Air Corps, under the new Chief Major General Oscar Westover. On the death of Westover in an air accident in September 1938 Arnold took over as Chief of the Air Corps and was immediately bumped to Major General. His first move was to push the R&D efforts much harder, especially over the new B-17 and the JATO concept. Happy to use civilian expertise, Caltech was an especial beneficiary of Air Corps funds and Theodore von Kármán of GALCIT developed a good working relationship with Arnold. Charles Lindbergh was also briefly co-opted by the Air Corps, as a spokesman for aviation. Arnold concentrated on rapid returns from R&D, expanding proven technologies to provide operation-orientated solutions to meet the rising threat, but from 1940 Arnold also pushed for jet propulsion, especially after the British gifted the plans of the Whittle turbojet in 1941.
With conflict approaching the separation between the Air Corps and the Air Force Combat Command was removed and the two were merged as the United States Army Air Forces. Arnold was made Chief of the Army Air Forces in June 1941. Even before then he pushed for aid to Britain and when the US began flying from England Arnold flew there to organize the 8th Air Force's campaign. He was a strong supporter of strategic rather than tactical bombing.
In March 1942 he was promoted to Commanding General, and was also given places on the decision making Joint Chiefs of Staff and the Combined Chiefs of Staff. On December 21, 1944 he was made a General of the Army, ranking him fourth in the US military structure.
After suffering a heart-attack he retired on June 30, 1946 after 43 years and was succeeded by Spaatz.
The United States Air Force was created in 1947 and on May 7, 1949 Arnold was honored by being made the first General of the Air Force.
He died in Sonoma, California and is buried in Arlington National Cemetery.
His nickname Hap was short for Happy, a nickname he picked up in the 1930s replacing his West Point gained nickname of Pewt.