Hamilton was born on March 24, 1916, in Uppsala, Sweden, to Dr. Bengt Leopold Knutsson Hamilton and Elise Franzisca Hamilton (née Neovius). On September 27, 1924, he boarded the S/S "Stockholm" with his mother and three sisters at the Port of Gothenburg, Sweden; the ship arrived at the Port of New York on October 6, 1924. The family's destination was Boston, Massachusetts, where they joined his father, Doctor Hamilton. Donald attended the University of Chicago (receiving a Bachelor of Science degree in 1938), and served in the United States Navy Reserve during World War II. He was married to Kathleen Hamilton (née Stick) from 1941 until her death in 1989. The couple had four children: Hugo, Elise, Gordon, and Victoria Hamilton.