Born in Derby, Roberts was educated at the University of Sheffield where he gained his PhD in 1968. He moved soon after to America and, after spending a year at Harvard, he moved to the Cold Spring Harbor Laboratory, New York, in 1971. He is currently serving as research director at New England Biolabs, Beverly, Massachusetts.

By the late 1970s it had become clear that the cells of some organisms seemed to have far too much DNA. Prokaryotic cells, i.e., cells without a nucleus, such as the bacteria Escherichia coli, have a single chromosome consisting of about 3 million DNA bases. A protein of about 300 amino acids will require 900 base pairs. Consequently a prokaryotic cell should be able to produce about 3000 proteins, a figure in reasonable agreement with experience. Eukaryotic cells, however, i.e., cells with a nucleus, as in mammals, have a genome of 3–4 billion base pairs, capable of producing some 3 million proteins, a number far in excess of the 150,000 or so proteins found in mammals. The disparity was solved in 1977 when Roberts, working with adenoviruses, stumbled upon the phenomenon of split genes. While all the DNA of prokaryotic cells was transcribed into messenger RNA (mRNA), which was then used as a template upon which amino acids could be assembled into proteins, something quite different seemed to be happening in the nuclei of eukaryotic cells. Only a part of the DNA, sometimes as little as 10%, was actually transcribed into mRNA. DNA appeared to be composed of several stretches, termed ‘introns’, serving no known purpose, but which separated the active DNA sequences, soon to be called ‘exons’. In the process of transcription the introns were neatly excised and the exons consequently spliced together to form the mature mRNA responsible for the production of protein.

The work of Roberts was independently confirmed by Phillip Sharp, with whom he shared the 1993 Nobel Prize for physiology or medicine.