Professor Wilmut, of Edinburgh University, shot to fame, but also drew criticism from some religious groups and pro-life campaigners after being involved in the cloning of the first mammal from an adult cell in 1996.
However, now he has decided to switch to a method pioneered by Professor Shinya Yamanaka at Kyoto University, Japan, who has managed to create stem cells from fragments of skin in mice without using embryos.
Prof Wilmut said that the new technique was "easier to accept socially" than the therapeutic cloning process he helped to establish.
The new method does not entail the use of human embryos, negating an ethical concern mentioned by the religious right and others against the stem-cell research.
"I decided a few weeks ago not to pursue nuclear transfer [the method by which Dolly was cloned]," the Scotsman quoted him, as saying.
Some scientists say that the overall success rate of the method used on Dolly the Sheep is too inefficient to be used in humans, particularly given the difficulties of obtaining eggs.
However, Prof Wilmut's decision will come as a blow to scientists who believe that the use of embryos to create stem cells is the best way to develop treatments for serious medical conditions, such as stroke, heart disease and Parkinson's disease.