Dunrossil took office on 2 February 1960. He was the first governor-general since Isaac Isaacs (1931–1936) to wear the full ceremonial viceregal uniform, but despite this was known for having a more relaxed approach than his predecessor. Dunrossil suffered from ill health while in office, and his wife frequently deputised for him at ceremonial events. He suffered a pulmonary embolism on the morning of 3 February 1961, becoming the first and only governor-general to die in office. He was granted a state funeral, and buried at St John the Baptist Church, Reid. His Official Secretary throughout his term was Murray Tyrrell.