Admiral Wiley was born in Troy, Alabama, on 31 January 1867. When he was sixteen years of age, he was appointed a Naval Cadet to the Academy on 17 May 1883, from the Fifth Congressional District of Texas by the Honorable James Webb Throckmorton. He graduated in 1888 and, prior to the Spanish-American War, had consecutive duty in the US Ships Mohican, Vandalia, Independence, San Francisco, Charleston, Ranger, Blake, Eagre and Gedney. In 1889 the Vandalia was lost in a hurricane at Apia, Samoa, and Naval Cadet Wiley was among those commended by the Commanding Officer for doing "their duty in the most commendable manner, distinguishing themselves for coolness, zeal, and pluck."
From April to August, 1898, in the grades of Ensign and Lieutenant (junior grade) he served as executive officer of the USS Maple, engaged in the blockade of Cuban ports. Following that duty he served in the Nautical School Ship, St. Mary's from October, 1898, to November, 1900. After assisting in training the crew of the battleship Wisconsin, he joined her when she was commissioned at San Francisco, 4 February 1901, and served in her until March, 1904. The Wisconsin operated off the west coast and visited Panama and Colombia before proceeding to the Asiatic Station. From March, 1904, to February, 1905, he was in command of the gunboat Villalobos on the Yangtze patrol of the Asiatic Station. After returning to the United States, he was on duty as discipline officer at the Naval Academy for a few months, and then served as executive officer of the Naval Training Station at Newport, Rhode Island, from April, 1906, to December, 1907.
Admiral Wiley, with the rank of Lieutenant Commander, was executive officer of the USS Kentucky during the world cruise with the Battle Fleet, 16 December 1907, to 22 February 1909. Upon completion of that cruise he reported for duty in the Bureau of Navigation, Navy Department, Washington, DC. Early in 1912, with the rank of Commander, he returned to the Asiatic Station where he had consecutive command of the USS Monterey and the USS Saratoga, (formerly the USS New York and later renamed the USS Rochester) operating as flagship of Rear Admiral Reginald F. Nicholson, Commander in Chief, Asiatic Fleet.
Admiral Wiley was a member of the Board of Inspection and Survey, Navy Department, from April, 1914, to December, 1915, and on 23 April 1915 he was promoted to the grade of Captain. On 1 January l916, he assumed command of the USS New Jersey, and later transferred to command of the battleship Wyoming which, with other vessels of Battleship Division 9, under command of Admiral Hugh Rodman, joined the British Grand Fleet on 7 December 1917, forming the Sixth Battle Squadron. Of that service Admiral Rodman reported, "From that day, we took part in every major operation in the North Sea, and some independent smaller ones. There was never a time but that we were ready when called upon. We could always steam full speed, maintain our position, and we received nothing but the highest praise, not only from the British admirals, officers and men, but from those of our Navy who visited us."
For service in the Wyoming, Admiral Wiley was awarded the Distinguished Service Medal with the citation:
"For exceptionally meritorious service in a duty of great responsibility in command of the USS Wyoming, operating in the War Zone in association and cooperation with the British Grand Fleet."
He was selected for promotion to the grade of Rear Admiral on 30 September 1918, and received promotion (temporary) to that rank on 28 November 1918. His commission for permanent promotion to Rear Admiral was issued 27 May 1921.
Admiral Wiley reported for duty as Commander, Division A, Battleship Force, Atlantic Fleet, on 23 October 1918. Early in 1919, he was transferred to duty as Commander, Division B, Battleship Force, Atlantic Fleet, and later of Division 4, of that fleet. While holding that command, he was appointed American Member of an Allied Commission to enforce the Naval terms of the Peace. His next duty was Commander, Destroyer Squadrons, US Pacific Fleet, from August, 1919, to December, 1920, when he reported at the Naval War College, Newport, Rhode Island, for instruction in the senior course. He served as Commandant of the First Naval District and the Boston Navy Yard from 31 December 1921, until 15 May 1923, and, during his next tour of sea duty, 20 June 1923, until 26 August 1925, served as Commander, Battleship Divisions, Battle Fleet, with the rank of Vice Admiral. He became a member of the General Board in October, 1925, and on 8 November 1927, hoisted his four star flag as Commander in Chief, US Fleet, with the rank of Admiral. Admiral Wiley continued duty as Commander in Chief until 21 May 1929, and on 30 September 1929, was transferred to the Retired List of the Navy at his own request upon completion of more than 46 years' service.
In 1936 President Roosevelt appointed Admiral Wiley as a member of the Maritime Commission for a term of four years.
In October, 1941, Admiral Wiley was recalled to active duty in the Office of Public Relations. He later served as Chairman of the Navy Board for Production Awards which reviewed recommendations from the Bureaus of the Navy Department and awarded the Army-Navy Production Award to industrial plants for excellence in the production of war material. In November, 1942, he was transferred to duty in the Office of the Chief of Naval Personnel and on 2 January 1943, he was relieved of all active duty.
He died on 20 May 1943, at Palm Beach, Florida, and was buried in the Arlington National Cemetery, Arlington, Virginia, on 24 May 1943.
In addition to the Distinguished Service Medal he received the Spanish Campaign Medal, the Sampson Medal, the Victory Medal, Grand Fleet Clasp, and the American Defense Service Medal. He was awarded the decoration of Commander of the Order of Leopold by the King of the Belgians.
A destroyer, the USS Henry A. Wiley, named in honor of Admiral Wiley, will be sponsored by his daughter.