If successful, they believe it could lead to a revolution in regenerative medicine.
The operation, lasting nearly nine hours, took place at London's Great Ormond Street children's hospital on Monday.
Stem cells taken from the boy's bone marrow were injected into the fibrous collagen 'scaffold' of a donor trachea, or windpipe.
The organ, which had first been stripped of its own cells, was then implanted into the boy.
Over the next month doctors expect the stem cells to begin transforming themselves within the boy's body into internal and external tracheal cells.
The boy, whose identity is being kept secret at the moment, is said to be doing well and talking from his hospital bed.
Because they are derived from his own tissue, there is no danger of the newly grown cells triggering an immune response.
With a normal transplant, rejection of the organ would necessitate dampening down the child's immune system with suppressive drugs.
At this early stage, his new windpipe is still having to be artificially supported.
Cardiothoracic surgeon Professor Martin Elliott, director of tracheal services at Great Ormond Street, who led the boy's operation, said: 'The child is extremely well.
'He's breathing completely for himself and speaking, and he says it's easier for him to breathe than it has been for many years.'The procedure was a big step forward from the pioneering surgery conducted in Spain two years ago on 30-year-old mother-of-two Claudia Castillo, the first person to receive a transplant organ created from stem cells.
Ms Castillo was given a section of tracheal airway rebuilt from stem cells, but using a much more complex and costly process.
On that occasion doctors grew the new tissue outside the body by rotating the donor graft in a special 'bioreactor' before transplanting it into the patient's body.
In the boy's case, his own body acted as a living bioreactor.
The de-cellularised windpipe was treated with a carefully mixed cocktail of chemicals designed to trigger signals that would allow the tissue to grow in situ.
Professor Martin Birchall, head of translational regenerative medicine at University College London, said: 'This procedure is different in a number of ways, and we believe it's a real milestone.
'It is the first time a child has received stem cell organ treatment, and it's the longest airway that has ever been replaced.
'I think the technique will allow not just highly specialised hospitals to carry out stem cell organ transplants.
'Now we need to conduct more clinical trials to demonstrate that this concept works. We'd like to move to other organs as well, particularly the larynx and oesophagus.
'Importantly we need to think about how to make regenerative medicine a key part of our health care.'
Preparation of the donor organ was carried out in the Great Ormond Street operating theatre by stem cell pioneer Professor Paolo Macchiarini, from Careggi University Hospital in Florence.
Prof Macchiarini led the Italian, British and Spanish team behind Ms Castillo's transplant.
Last year he carried out the 'living bioreactor' stem cell procedure for the first time on a 53-year-old Italian woman, replacing part of her windpipe.
The successful operation proved that the concept worked.
Prof Macchiarini was contacted by British doctors after they ran out of options for helping the boy patient, who was born with a condition called long segment tracheal stenosis.
At birth the boy had a windpipe measuring just one millimetre across and was unable to breath.
Attempts were made to patch up his trachea and hold it open with supporting stents.
But eventually the stents eroded, damaging the aorta, the main artery taking blood out of the heart.
Moves towards carrying out the experimental procedure began after the boy's condition deteriorated last November.
In February this year, Prof Macchiarini's team selected a dead donor from a shortlist of three - a 30-year-old Italian woman.
Her trachea was removed, and stripped of its cells using digestive enzymes. All that was left was inert collagen and the 'basal membrane' which provided the foundation for cell growth.
Prof Macchiarini joined his British colleagues at Great Ormond Street on the day of the operation, where he took charge of 'seeding' the trachea with the stem cells and applying the correct 'growth factor' chemicals.
In Ms Castillo's case it took six months to prepare the transplant organ outside the patient's body.
But using the new 'bionic' technique, the boy's trachea was ready to be implanted in just four hours.
Prof Macchiarini said: 'The idea is to use the reactions of the body to make the structure living.
'We told the cells to differentiate and transform naturally into the layers that make up the airway.
'This is something that makes tissue regeneration very simple and accessible to everyone.'
He said the implications for future treatments went beyond replacing whole organs.
Damaged organs such as lungs, hearts or livers could be repaired by patching them with stem cells.
'We need to change our philosophy,' said Prof Macchiarini, speaking at University College London.
'The question is do we really need to transplant the entire organ and put the patient on immunosuppression, or can we stimulate stem cells to make it function again?'
The piece of windpipe that was grown to replace Claudia Castillo's damaged organ
Professor Martin Birchall, head of translational regenerative medicine at UCL, left, and Professor Paolo Macchiarini, from Careggi University Hospital in Florence
Members of the team who performed the groundbreaking operation (left to right) Prof Martin Birchall, Dr Mark Lowdell, Prof Paolo Macchiarini and Prof Martin Elliott outside UCL today
