The world's first baby born from a transplanted womb is soon to have company - two more women who became pregnant after having transplants are due in the next few weeks.

It could be the start of a new wave of babies born this way, say the Swedish doctors who pioneered the technique.

"It means a lot to me that we are able to help patients who have tried for so long to have families," said Dr Mats Brannstrom, a professor of gynaecology and obstetrics at the University of Gothenburg, who led the project that brought about last month's pioneering birth.

"This is the last piece of the puzzle in finding a treatment for all women with infertility problems."

Dr Brannstrom predicted there would soon be many more babies born to women who have received donated wombs in countries where doctors are studying the technique, including Australia, Britain, the US, Japan and China.

He said he has also started work on trying to grow a womb in the lab. That involves taking one from a deceased donor, stripping it of its DNA and using cells from the recipient to line the structure.

He has started preliminary tests in animals and estimated it would be another five years before the technique can be tried on humans.

While that may sound like science fiction, the techniques that led to the birth announced last week also sounded outlandish just years ago.

The happy couple in Sweden named their son Vincent, which means "to conquer", to celebrate a victory over their difficult journey to parenthood.

The mother has said she still cannot believe she is a mother, after discovering at 15 that she had no womb and being told that she would never carry her own children.

Now 36, she was one of nine women to receive a transplanted womb last year in a ground-breaking trial led by Dr Brannstrom.

Her husband said the couple, who want to remain anonymous, will be forever grateful to the 61-year-old woman who donated her uterus, the mother of one of his best friends.

The woman - now the boy's godmother - made the offer after hearing about the difficulties the young couple was having in starting a family.

"What she did for us was so amazing and selfless that the words 'thank you' don't seem like enough," the father said.

The new parents said they have not quite worked out how they will tell their son that he made medical history when he is older.

"We will show him all the articles that were written and tell him everything we went through to get him," she said. "Maybe he will be inspired to become a doctor."

The couple hope they can be an inspiration to others struggling with infertility, but say that is not why they did it.

"Yes, we're the first to do this, but that's not the important thing," the mother said.