"We hold Bob in great affection and are delighted to send our personal congratulations to him and his family at this time."
Her parents, Lesley and John, had been trying to have children for nine years but could not because Lesley Brown's fallopian tubes were blocked.
But thanks to Edwards' work in developing in-vitro fertilisation (IVF), Louise was born at Oldham and District General Hospital in north-west England, weighing five pounds 12 ounces (2.61 kilograms) on July 25, 1978.
The IVF procedure entails taking an egg from a woman and fertilising it in a lab dish with sperm donated from a man.
The egg divides, is allowed to develop into an early-stage embryo and is then inserted in the woman's uterus where, if all goes well, it will become a baby.
The Vatican criticised the decision to honour Edwards with the head of the Pontifical Academy for Life, which speaks for the Vatican on medical ethics issues, describing the move as "completely out of order".
"Without Edwards, there would not be a market on which millions of ovocytes are sold... and there would not be a large number of freezers filled with embryos in the world," ANSA news agency quoted Ignacio Carrasco de Paula as saying.
"In the best of cases they are transferred into a uterus but most probably they will end up abandoned or dead, which is a problem for which the new Nobel Prize winner is responsible," he added.
In a toned down transcript of the interview with ANSA, he said the choice was understandable and specified he was speaking in a personal capacity.
After getting his doctorate in 1955 at Edinburgh University, the Manchester-born Edwards then began working on developing the IVF process, first studying germ cells in animals.
Since Brown's birth, nearly four million people have been born through IVF.
"His achievements have made it possible to treat infertility, a medical condition afflicting a large proportion of humanity including more than 10 percent of all couples worldwide," the Nobel Assembly at the Swedish Karolinska Institute said.
Edwards is too frail to give interviews but his wife Ruth said the family was "thrilled and delighted" at the honour.
He has in the past described how controversial his work had been.
"I was called crazy," he told Swedish news agency TT five years ago.
"No one wanted to take the ethical risk. People told me the child would not be normal and wondered what I would do then. But I was never worried, my research had showed that IVF worked just like natural conception," he said.
Edwards worked closely with British gynecologist Patrick Steptoe, who died in 1988. Together they established the Bourn Hall Clinic in Cambridge, the world's first centre for IVF therapy.
After he won the prestigious Albert Lasker award in 2001, Edwards told US broadcaster CBS he and Steptoe "never thought the embryos would be born abnormal, even though famous people, including Nobel Prize winners, told me that I would have to do infanticide on the babies."
Today, 20 to 30 percent of eggs fertilised by IVF lead to the birth of a child.
"Long-term follow-up studies have shown that IVF children are as healthy as other children," the Nobel jury said, pointing out that Louise Brown and a number of other IVF children have naturally given birth to children themselves.
Edwards will receive a medal and 10 million Swedish kronor (1.49 million dollars, 1.09 million euros).
The Medicine Prize kicked off a week of prestigious award announcements, with the two most watched, Literature and Peace, to be announced on Thursday and Friday.