Born in Falmouth, Kentucky, Sharp was educated at Union College, Kentucky, and the University of Illinois, Urbana, where he obtained his PhD in 1969. After spending short periods as a postdoctoral fellow at Caltech and Cold Spring Harbor Laboratory, New York, Sharp joined the Massachusetts Institute of Technology in 1974 and was appointed professor of biology in 1979.

Much of the early work in molecular genetics had been carried out on prokaryotes, cells that lack a nucleus. It was found that continuous stretches of DNA were converted into various proteins. The DNA was first transcribed into a continuous sequence of messenger RNA (mRNA), triplets of which coded for one of the amino acids from which proteins were assembled. It was automatically assumed that similar mechanisms would be found to operate in eukaryotic cells, cells with a nucleus.

In 1977, however, Sharp demonstrated that this assumption was baseless. Sharp worked with adenoviruses, the viruses responsible for, among other things, the common cold. He explored the process of protein production by forming double stranded hybrids of adenovirus DNA and mRNA. The hybrids were then displayed on an electron micrograph. To Sharp's surprise the mRNA hybridized with only four regions of DNA, and these were separated by long stretches of DNA looping out from the hybrid. The intervening loops, later to be termed ‘introns’ by Walter Gilbert, it was presumed, were later snipped off and the four remaining groups, ‘exons’ in Gilbert's terminology, would be spliced together to form the mature mRNA. This mature mRNA would then leave the cell's nucleus and serve as the template upon which proteins could be assembled.

Sharp's work was confirmed independently by Richard Roberts. The ‘split genes’ identified in adenoviruses by Sharp were quickly shown to be fairly standard in eukaryotic cells. The phenomenon has proved highly puzzling. In some organisms as much as 90% of nuclear DNA is snipped away as introns and consequently seems to serve no purpose at all. Why there should be so much ‘junk’ DNA as it has sometimes been described remains a mystery.

For his discovery of split genes Sharp shared the 1993 Nobel Prize for physiology or medicine with Richard Roberts.