Doctors said the womb came from a living donor who does not know the patient.
A womb transplant program at Baylor has been under way since a year ago, and surgeons there have completed eight in a medical trial of 10 transplants, according to Time.
Doctors will remove the transplanted uterus after the first or second pregnancy because the mother can't stay on anti-rejection drugs indefinitely.
They're monitoring the baby and say he is breathing and eating well. "It was a very exciting birth".
Experts agree results of the clinical trial could help women who are born without a uterus, lost their uterus or no longer possess function of the female organ.
Since then, the Swedish hospital has had a total of eight babies born to mothers who've received uterine transplants.
The first attempted uterus transplant in the United States in February 2016 at the Cleveland Clinic in OH, from a deceased donor, failed because of a yeast infection. The wombs are not meant to be permanent.
Baylor has had a study underway for several years to enroll up to 10 women for uterus transplants.
A 36-year-old registered nurse who has two children donated her uterus to the unnamed woman, Time said.
The birth of the healthy baby, whose birth date, sex and weight were not disclosed, was confirmed by a spokesman for the Baylor University Medical Center.
The first birth as a result of a womb transplant in the United States has occurred in Texas, a milestone for the US but one achieved several years ago in Sweden.
When a woman has a transplanted uterus, in vitro fertilization is the only way she can become pregnant because the ovaries are not connected to the transplanted womb.
While the birth of a healthy baby by a woman with a transplanted uterus was a medical first in the United States, it follows several childbirths by women with transplanted uteruses at Sahlgrenska University Hospital in Gothenburg in Sweden, said Civale.
And for most of their lives many had been told that they wouldn't be able to have children. "What I've learned emotionally, I do not have the words to describe".