The researchers have grown fresh layers of bone on existing healthy leg bones and then transplanted the new tissue to mend bones in other parts of the body.
The research has been carried out on laboratory rabbits but the scientists believe they will soon be able to perform similar operations on humans.
As well as providing a new and abundant source of fresh bone tissue, the technique of self-transplant surgery would minimise the risk of introducing infections, and overcome the need for the patient to take tissue-rejection drugs.
Molly Stevens of Imperial College London, who was part of the international team who carried out the research, said the breakthrough was among the most important in the field of bone regeneration for many years.
"We're really excited because it deviates so much from the previous approaches and the results are so much better," she said.
"All the other approaches to the engineering of new bone tissue haven't worked and this approach of taking bone from the same patient means there should be no problems of rejection or infection," she said.
Bone surgery is seriously hampered by the lack of fresh bone tissue for transplants. The conventional approach is to take small pieces of bone from the patient's hip or ribs, but the amount that can be taken is limited and the procedure is painful and risky.
A more revolutionary approach is to grow bone artificially in the laboratory, but this has proved disappointing the amount that can be grown is limited and its internal structure is weak.
The latest technique is to grow new bone inside the body using our inherent bone-growing tissue a thin membrane that surrounds the bone called the periosteum which contains the vital stem cells of the bone.
The scientists injected a sterile saline solution underneath the periosteum to create a small fluid-filled cavity between the membrane and the surface of the bone. They then injected a gel containing calcium, which stimulated stem cells in the periosteum to produce layers of fresh bone.
Prasad Shastri, assistant professor of biomedical engineering at Vanderbilt University in Nashville, Tennessee, said the process was akin to creating a miniature "bone bioreactor" inside the body. "We have shown that we can grow predictable volumes of bone on demand. And we did so by persuading the body to do what it already knows how to do," Professor Shastri said.
Dr Stevens said it was relatively easy to peel away the freshly grown layers of bone without damaging the tibia or shinbone beneath.
"The new bone actually has comparable strength and mechanical properties to native bone and since the harvested bone is fresh it integrates really well at a recipient site," she said.
The study, published in the journal Proceedings of the National Academy of Sciences, has already formed the basis of an application to a hospital ethics committee for human trials.
The trials are also being studied with a view to adopting a similar approach for the engineering of fresh liver and pancreatic tissue, organs that also have outer layers similar to a periosteum, said Professor Robert Langer of the Massachusetts Institute of Technology in Boston who was also part of the research team.
It took six weeks for the new layers of bone to form in the rabbits, and another 12 weeks or so for the transplants to fuse with and repair the damaged bones.