The 10-hour transplant operation - and later fertility treatment - took place in São Paolo, Brazil, in 2016. The mother, 32, was born without a womb.
There have been 39 womb transplants using a live donor, including mothers donating their womb to their daughter, resulting in 11 babies.
But the 10 previous transplants from a dead donor have failed or resulted in miscarriage.
In this case, the womb donor was a mother of three in her mid-40s who died from bleeding on the brain.
The recipient had Mayer-Rokitansky-Küster-Hauser syndrome, which affects about one in every 4,500 women and results in the vagina and uterus (womb) failing to form properly.
However, her ovaries were fine. And doctors were able to remove eggs, fertilise them with the father-to-be's sperm and freeze them.
The woman was given drugs that weakened her immune system to prevent her body attacking and rejecting the transplant.
And about six weeks later, she started having periods.
After seven months, the fertilised eggs were implanted.
And, after a normal pregnancy, a 6lb (2.5kg) baby was delivered by Caesarean section on 15 December 2017.
Dr Dani Ejzenberg, from Hospital das Clínicas in Sao Paolo, said: "The first uterus transplants from live donors were a medical milestone, creating the possibility of childbirth for many infertile women with access to suitable donors and the needed medical facilities.
"However, the need for a live donor is a major limitation as donors are rare, typically being willing and eligible family members or close friends."
Dr Srdjan Saso, from Imperial College London, said the results were "extremely exciting".
"It enables use of a much wider potential donor population, applies lower costs and avoids live donors' surgical risks."