During World War II, he served in the United States Navy. Appointed by Democratic president John F. Kennedy to the Treasury post, Dillon was himself a Republican. His policies provided for a solid economic expansion and president Lyndon B. Johnson kept him in his job after Kennedy's assassination.
The family descends from his grandfather Samuel Lapowski, a poor immigrant from Poland, who changed the family name from Lapowski to Dillon ("Samuel Dillon"). Dillon's mother, Anne Douglass, is descended from Grahams Lairds of Tamrawer Castle at Kilsyth, Stirling, Scotland—see family tree link below.
Dillon served as President of the New York Metropolitan Museum, particularly building up its Chinese galleries. He personally donated $20 million to the museum and led a fundraising campaign that raised an additional $100 million. A close friend of John D. Rockefeller 3rd, he was also a trustee of the Rockefeller Foundation from 1960 to 1961.
The Fifth Round of tariff negotiations under the General Agreement on Tariffs and Trade (GATT), which lasted from 1960 to 1962, was known as the "Dillon Round", after Dillon, who proposed its inception.
He received the Medal of Freedom in 1989.
Dillon was born in Geneva. At Boston, Massachusetts, on 10 March 1931, Dillon married his first wife, the former Phyllis Chess Ellsworth (South Bend, Indiana, 3 August 1910 – New York City, New York, 20 June 1982), daughter of John Chess Ellsworth (South Bend, Indiana, 20 December 1874 – living 1957) and wife (married at Lowell, Massachusetts, 14 October 1903) Alice Frances Chalifoux (Lowell, Massachusetts, 9 August 1881 – New York City, New York, 27 January 1957), who bore him two daughters: Phyllis Ellsworth Douglas Dillon and Joan Douglas Dillon (b. New York City, New York, 31 January 1935). She married firstly at Paris, 1 August 1953 (div. Washoe, Nevada, 12 December 1955, annulled Rome, 22 June 1963) James Brady Moseley (New York City, New York, 22 May 1931 – Boston, Massachusetts, 9 April 1998), son of Frederick S. Moseley, Jr. and wife Jane H. Brady. She married secondly at St. Edward's, Sutton Park, Guilford, Surrey, 1 March 1967, H.R.H. Charles Frédéric Louis Guillaume Marie, Prince de Luxembourg, Principe di Borbone di Parma (Château de Berg, Luxembourg, 7 August 1927 – Imbarcati, Prov. Pistoia, Italy, 26 July 1977), son of H.R.H. Felix of Bourbon-Parma, and wife H.G.D.H. Charlotte, Grand Duchess of Luxembourg, Herzogin von Nassau. She married thirdly at Isleboro, Maine, 3 August 1978, Philippe-François-Armand-Marie de Noailles, Duc de Mouchy, Prince-Duc de Poix (b. Paris, 17 April 1922), son of Henry Antoine Marie de Noailles, Duc de Mouchy, Prince-Duc de Poix, and wife Marie Françoise Nicole de La Rochefoucauld.
In 1983 Dillon married his second wife, the former Susan Sage (born 1917).