One of the unidentified women had her uterus removed many years ago because of cervical cancer, while the other was born without a womb. Both are in their 30s.
They will undergo a year of observation before doctors attempt to help them get pregnant via in vitro fertilization, in which embryos created with eggs from their own ovaries will be implanted in their wombs.
Researchers around the world have been looking for ways to transplant wombs so that women who have lost a uterus to cancer or other diseases can become pregnant.
Fertility experts hailed the Swedish transplants as a significant step but stressed it remains to be seen whether they will result in successful pregnancies.
Even if the approach works, it is unclear how many women will choose such an option, given the risks and the extreme nature of the operation compared with, say, using a surrogate mother.
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 is doing fine, but he wasn't sure whether she has started fertility treatment.
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.
Olausson said there could be a lower risk of organ rejection when the donor is a family member, but he said a more important factor is the "emotional connection" between mother and daughter.
Also, the mother-daughter procedure makes it easier to "know that the transplanted organ works," he said, adding that it doesn't matter whether the donor is past menopause.
For a year, doctors will monitor how the two patients respond to the anti-rejection drugs needed to stop their immune systems from attacking the donated wombs.
After a maximum of two pregnancies, the wombs will be removed so the women can stop taking the drugs, which can have side effects such as high blood pressure, swelling and diabetes and may also raise the risk of some types of cancer.
"There's no doubt this will be a pioneering step if it's been successful," said Scott Nelson, chairman of obstetrics and gynecology at the University of Glasgow, Scotland. "At present, the only option for these women is to have a surrogacy i.e., having their embryos implanted into another woman."
Nelson said a donated womb would not contain all the blood vessels it originally had, possibly compromising a baby's development.
"Pre-term birth is a major risk i.e., a small baby being born. That's what you'd mainly be worried about," he said.
James Grifo, an infertility expert at New York University, questioned how a fetus would be affected by the immune-suppressing drugs.
"Some people will always be willing to take the risk, but there are issues that need to be addressed before you expose a fetus to these medicines," he said. Grifo and colleagues at NYU abandoned a uterus transplant program "because some issues seemed insurmountable."
"The group of patients that would need this is so small we decided to focus our efforts elsewhere," he said. "We started in rats, but once we got to humans, it became very clear the rejection drug was going to be the issue, and we didn't know how to safely deal with that issue."
In Sweden, Olausson said anti-rejection drugs have not proved harmful to fetuses when the mother has undergone other organ transplants. Also, tests on mice, rats and pigs with transplanted wombs showed no ill effects from such drugs, he said.