The women were born without a uterus or had it removed because of cervical cancer. Most are in their 30s and are part of the first major experiment to test whether it's possible to transplant wombs into women.
Life-saving transplants of organs such as hearts, livers and kidneys have been done for decades and doctors are increasingly transplanting hands, faces and other body parts to improve patients' quality of life.
There have been two previous attempts to transplant a womb in Turkey and Saudi Arabia but both failed to produce babies.
"This is a new kind of surgery. We have no textbook to look at," Dr Mats Brannstrom told The Associated Press.
Brannstrom, chair of the obstetrics and gynaecology department at the University of Gothenburg is leading the initiative who will run the first-ever workshop on how to perform womb transplants and plans to publish a scientific report on his team's efforts soon.
Brannstrom said the nine womb recipients were doing well.
Many already had their periods six weeks after the transplants, an early sign that the wombs are healthy and functioning.
In Britain, doctors are planning to perform uterus transplants, but will only use wombs from dying or dead people.
"Mats has done something amazing and we understand completely why he has taken this route, but we are wary of that approach," said Dr Richard Smith, head of the U K charity Womb Transplant which is trying to raise USD 823,000 to carry out five operations in Britain.
Smith said the biggest question is how any pregnancies will proceed.
"What remains to be seen is whether this is a viable option or if this is going to be confined to research and limited experimentation," said Dr Yacoub Khalaf, director of the Assisted Conception unit at Guy's and St Thomas' hospital in London.