Elliott was born in Wellington into a family with a long medical history. His father, Sir James Elliott, was a doctor and medical journalist, editing the New Zealand Medical Journal for many years, and both of his brothers trained as doctors.
He was educated at Wanganui Collegiate School and later studied at Victoria University of Wellington and University of Otago Dunedin School of Medicine where he graduated with a Bachelor of Medicine Bachelor of Surgery in 1947.
During World World War II he served with the 1st Battalion, Wellington Regiment, and the Otago University Medical Corps. Elliott served the for many years and was Chancellor of Street John in New Zealand from 1980 to 1986. His father was also Chancellor of Street John.
He also performed several tours of duty to the Street John Eye Hospital in Jerusalem as Ophthalmic Surgeon.
Elliott was appointed an Officer of the Order of the British Empire in the 1976 New Year for services to medicine, especially ophthamology. In the 1977 Silver Jubilee and Queen"s Birthday, he was raised to Knight Commander of the Order of the British Empire, for services to medicine. In 1978, Elliott was appointed a Knight of the He was promoted to Bailiff Grand Cross of the in 1987 in recognition of his significant contribution to the order of Street John. His father was also promoted to Bailiff Grand Cross. Bailiff Grand Cross is the highest award in the Street John system. This honour is limited to only ten people, outside the Royal family, worldwide.
