Announcing the prize at the Karolinska Institute in Stockholm on 8 October, the Nobel Assembly said the scientists' findings had "revolutionised our understanding of how cells and organisms develop".
The work has led to a new field of medicine using pluripotent stem cells, adult cells that have been reprogrammed to be able to develop into any cell type.
Pluriporent stem cells are of interest in research for their potential to create new medicines and disease models without the need to use embryonic tissue, which remains controversial in many parts of the world.
While working on the cloning of frogs at the University of Oxford in 1962, Sir John discovered that the specialisation of cells is reversible, and that mature cells still contain all the information needed to develop into any cell in the body.
Some 40 years later, in 2006, Professor Yamanaka discovered how mature cells in mice could be reprogrammed to become able to develop into any cell type.
Sir John has also previously served as professor of cell biology and master of Magdalene College at Cambridge and as a member of the Nuffield Council on Bioethics.
The prize in physiology or medicine is the first of the Nobel Prizes to be issued this year, with prizes in physics, chemistry and peace to be announced later this week.