The parents of the first baby born to a woman who had received a womb transplant said they hoped they could be an inspiration to others struggling with infertility.

After what they described as a rollercoaster journey, the unnamed Swedish couple finally became parents last month, when the mother gave birth to a healthy, though premature, baby boy.

For the couple, making history was an afterthought.

"Yes, we're the first to do this, but that's not the important thing," the mother told the Associated Press at their home in an undisclosed part of Sweden. "I want people to know that what they think is impossible can happen."

To mark their baby's birth as a victory over their difficult journey to parenthood, they named him Vincent, meaning, "to conquer".

Cradling her sleeping young son, she said she still could not believe she was finally a mother, after being told at age 15 that she had no uterus and would never carry her own children. Now 36, the woman was one of nine to receive a transplanted uterus last year in a groundbreaking trial led by Dr Mats Brannstrom, a professor of gynecology and obstetrics at the University of Gothenburg and Stockholm IVF.

Based in Gothenburg, Brannstrom said his patients are from all over Sweden. Aside from his efforts, two other such transplants have previously been tried - in Saudi Arabia and Turkey - but neither has resulted in a live birth.

For the new mother, the normal stresses of caring for a newborn seem less important after years of thinking she would never have a child.

"We've been through so many things I couldn't control but now that this little fantastic boy is here, I just feel relieved," she said, in a near-spotless, stylish two-floor house that bore little trace of a newborn except for an errant pacifier on the kitchen counter.

Her husband said they will be forever grateful to the 61-year-old woman who donated her uterus, the mother of one of his best friends. She 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," said the father, adding that the donor is also the godmother to their son.

These days, the new parents are busy marveling at their baby's expressive face and remarkably calm nature.

"He doesn't really scream, but he makes these funny little sounds," the mother said, comparing him to a kitten. Though his white wooden crib has a welcoming teddy bear and blankets, she said her son prefers to sleep between his parents in their bed.

She and her husband said they haven't quite figured out how to tell their son how he made medical history, once he's older.