Among those who acclaimed the award were Britain's Royal Society, Ian Wilmut, "father" of Dolly the cloned sheep, and a leading ethicist, who said it eased a storm about the use of embryonic cells.
Stem cells are precursor cells which differentiate into the various organs of the body.
They have stirred huge excitement, with hopes that they can be coaxed into growing into replacement tissue for victims of Alzheimer's, Parkinson's and other diseases.
Gurdon, 79, said he was grateful but also surprised by the honour, since his main research was done a half-century ago.
In 1962, he discovered that the DNA code in the nucleus of an adult frog cell held all the information to develop into every kind of cell.
This meant that an adult cell could in essence be reprogrammed.
His landmark discovery was initially met with scepticism, as the journey from immature to specialised cell was previously deemed irreversible.
"I'm amazed and immensely grateful and astonished that they should recognise work done such a long time ago," Gurdon told Swedish Radio.
He later told reporters in London his groundbreaking work "was essentially to show that all the different cells of the body have the same genes.
"The work that I did was to test that proposition ... The outcome was that they do," he said.
"It is particularly pleasing to see how purely basic research, originally aimed at testing the genetic identity of different cell types in the body, has turned out to have clear human health prospects," he said.
Based at Cambridge University, Gurdon is fond of recalling that his school tutor told him when he was 15 that it would be a "total waste of time" to pursue a career in science, and credits his mother with encouraging him to follow his passion.
More than four decades later, in 2006, Yamanaka, now 50, discovered how mature cells in mice could be turned back to their youthful state using a batch of reprogramming genes.
The advantage of this would be to avert the need to use stem cells taken from early-stage embryos. These are hugely versatile but have stirred ethical controversy.
"This is not only a giant leap for science, it is a giant leap for mankind. Yamanaka and Gurdon have shown how science can be done ethically," a professor of practical ethics at the University of Oxford, Julian Savulescu, told the Science Media Centre in London.
Yamanaka "deserves not only a Nobel Prize for Medicine, but a Nobel Prize for Ethics," he said.
Yamanaka, a professor at Kyoto University, has pointedly warned of the ethical controversies of science.
"We should limit the application of technology to treatment or what can make patients happier," he has said. "We may be able to generate new life (with this technique), so we are presented with another ethical issue."
Stem-cell research is still at a very early stage, and only a tiny number of human trials have taken place.
In the field of so-called induced pluripotent stem (iPS) cells, for which Yamanaka was singled out for the Nobel, work is still only in the lab.
He was modest about the honour on Monday, telling reporters he was "just an obscure researcher" who planned to carry on his work.
"I really feel that I have to realise a medical application and contribute to society as soon as possible," he said.
The pair had been among the frontrunners for a Nobel after they won the prestigious Lasker Prize in 2009 and Yamanaka shared the 1.2-million-euro Millennium Technology Prize earlier this year with a software engineer.
Because of the economic crisis, the Nobel Foundation has slashed its prize sum to eight million Swedish kronor ($1.2 million, 930,000 euros) per award, down from the 10 million kronor awarded since 2001.
On Tuesday, the winners of the physics prize will be announced, followed by the chemistry prize on Wednesday and the literature prize on Thursday.
The peace prize will be announced Friday and the economics prize will wind up the Nobel season on October 15.
The laureates will receive their prizes at formal ceremonies in Stockholm and Oslo on December 10, the anniversary of prize founder Alfred Nobel's death in 1896.