Specialists at the University of Goteborg completed the surgery over the weekend without complications, but say they won't consider the procedures successful unless the women achieve pregnancy after their observation period ends a year from now.
"We are not going to call it a complete success until this results in children," said Michael Olausson, one of the Swedish surgeons told The Associated Press. "That's the best proof."
He said the daughters started in-vitro fertilization, or IVF, before the surgery.
IVF uses hormones to stimulate the ovaries, which the women already had, to produce eggs. Scientists would fertilize the eggs with sperm in a lab, before freezing the embryos. The frozen embryos would then be thawed and transferred if the women are in good health after the observation period, Olausson said. After a maximum of two pregnancies, the wombs will be removed again.
The university said one recipient had her uterus removed many years ago due to cervical cancer and the other was born without a uterus. Both women are in their 30s.
"Both patients that received new uteri are doing fine but are tired after surgery. The donating mothers are up and walking and will be discharged from the hospital within a few days," team leader Mats Brannstrom said in a statement.
Turkish doctors last year said they performed the first successful uterus transplant, giving a womb from a deceased donor to a young woman. Olausson said that woman was doing fine, but he wasn't sure whether she had started undergoing fertility treatment yet.
In 2000, doctors in Saudi Arabia transplanted a uterus from a live donor, but it had to be removed three months later because of a blood clot.
Scott Nelson, chair of obstetrics and gynecology at the University of Glasgow, called the Swedish transplants a "huge step" but stressed it remains to be seen whether they result in successful pregnancies.
"In terms of the risk to the pregnancy, the greatest concerns are the placenta not developing normally, the baby not growing properly and being born prematurely," said Nelson, who was not involved with the transplants. "Pre-term birth is a major risk, i.e. a small baby being born, that's what you'd mainly be worried about."