He attended Gravesend Grammar School (1926–29), The King's School, Rochester (1929–32), Tonbridge School (1932–35) and Medway Technical College (1937–39). In 1938 he entered Imperial College London, where he graduated in 1940 and obtained his PhD degree in Organic Chemistry in 1942.
From 1942 to 1944 he was a government research Chemist, from 1944 to 1945 he was with Albright and Wilson in Birmingham. He then became Assistant Lecturer in the Department of Chemistry of Imperial College, and from 1946 to 1949 he was ICI Research Fellow.
In 1949 he was the first recipient of the Corday-Morgan Medal and Prize awarded by the Royal Society of Chemistry. In 1954 he was elected a Fellow of the Royal Society and the International Academy of Science as well as, in 1956, a Fellow of the Royal Society of Edinburgh; in 1965 he was appointed member of the Council for Scientific Policy. He was knighted in 1972, becoming formally styled Sir Derek in Britain. In 1978 he became Director of the Institut de Chimie des Substances Naturelles (ICSN - Gif Sur-Yvette) in France.
Barton was elected a Fellow of the Royal Society (FRS) in 1954. In 1966 he was elected a Member of the German Academy of Sciences Leopoldina.
In 1958 Professor Barton was appointed Arthur D. Little Visiting Professor of Massachusetts Institute of Technology, and in 1959 Karl Folkers Visiting Professor of Illinois and Wisconsin Universities. In 1960 he was appointed a Visiting Professor of the University of California, Berkeley, spending much of his time with the W.H. Dauben Group. The same year he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences.
In 1986 he became Distinguished Professor at Texas A&M University and held this position for 12 years until his death.
In 1996, Professor Barton published a comprehensive volume of his works, entitled Reason and Imagination: Reflections on Research in Organic Chemistry.