Born to a well-to-do family in Yancheng county, Jiangsu province, Hau received a military education from the Chinese Military Academy, Chinese Army University, U.S. Army Command and General Staff College, and the War College, Armed Forces University. Hau was appointed an artillery officer in 1938, and served in the Chinese expeditionary forces in India during World War II. In the subsequent Chinese Civil War he was a staff officer.
As commander of the 9th Infantry Division from 1958 to 1961, Hau presided over the 44-day bombardment of Quemoy by the People's Liberation Army. He commanded the 3rd Corps from 1963 to 1965, served as Chief Aide to Chiang Kai-shek from 1965 to 1970. He continued his army career as Commander of the 1st Field Army from 1970 to 1973, Deputy Commander-in-Chief of the ROC Army from 1975 to 1977, Executive Vice Chief of the General Staff in the Ministry of National Defense from 1977 to 1978, Commander-in-Chief of the ROC Army 1978 to 1981, and Chief of the General Staff in the Ministry of National Defense from 1981 to 1989.
He was a member of the Central Standing Committee of the Kuomintang from 1984 to 1993 and served as Minister of National Defense from 1989 until 1990 when he was appointed Premier. He was appointed by President Lee Teng-hui in part to mollify the conservative mainlander faction within the KMT that had threatened to run a rival presidential ticket in the March 1990 election. Hau's appointment sparked protests by those who believed it marked retrogression toward military rule, while President Lee defended his decision by saying he valued Hau's tough stance on crime. As premier he held high approval ratings - he was tough on crime and promoted a multi-billion-dollar economic development plan to industrialize Taiwan. Hau submitted his resignation in January 1993 after the KMT's poor showing in the 1992 Legislative Yuan election.
Appointed as one of four vice-chairmen of the KMT in the 14th Party Congress in another effort by Lee to pacify the mainlander faction, Hau served from 1993 to 1995.
In the , he ran for vice-president as an independent on the ticket of Lin Yang-kang and had his KMT membership "cancelled" . His party membership was restored in 2005.
He married Kuo Wan-hua and has two sons and three daughters. One of his sons is politician Hau Lung-pin, the former chairman of the , and incumbent Mayor of Taipei.