"Although he wasn't with us very long, and we brought him into the world knowing there was no hope of a life for him, we are incredibly proud of his heroism," said Jess Evans, from Cardiff.
Evans was 12 weeks' pregnant with twins when she was told one of the sons she was carrying had a rare and fatal condition which prevents the brain and skull developing.
Evans and her fiance Mike Houlston were told their baby would either be stillborn or die very shortly afterwards.
But the couple were determined their son's life would be remembered and decided to allow his kidneys and heart valves to be donated so he could save the lives of others.
Their twins, Teddy and Noah Houlston, were born a year ago, but Teddy died after clinging to life for just 100 minutes. His kidneys have gone on to save the life of a patient with renal failure.
Houlston, 30, told the Daily Mirror: "He lived and died a hero. It's impossible to explain how proud we are of him."
Evans added: "We hope Teddy's story will inspire families who find themselves in the position of losing a child. Knowing part of your loved one is living on in someone else is comforting."
It is incredibly rare for newborns to be considered as donors and Dr Paul Murphy, of NHS Blood and Transplant, described Teddy's donation as "exceptional".
"Every donation is inspirational. It is a selfless act of heroism," he said.
"But Teddy's story is exceptional. He was the youngest organ donor in the UK."
The couple, who were childhood sweethearts, said discovering one of their sons would not survive was soul destroying.
They were offered the option to abort, but never considered it.
"We thought even if we had a moment with him, or 10 minutes, or an hour, that time was the most precious thing we would ever experience," said Evans.
They decided they wanted their baby to help someone in need of a transplant.
"It helps us so much to know he has helped someone else and helped doctors realise donation from small babies is possible and is something people like us want to make happen," said Evans, who also has a three-year-old daughter from a previous relationship.
Evans and Houlston are now fundraising for the charity 2 Wish Upon A Star, which provides services for bereaved parents.
On their JustGiving page they say: "Teddy Noah Houlston became an organ donor in the UK on 22 April 2014.
‘He was born with a condition called anencephaly, a terminal disability which meant Teddy was only with us for a very short period but in that time he was the perfect son, an inspirational brother to his twin Noah Teddy Houlston and a hero to his big sister Billie Grace.
"Teddys journey has just began, it is a never ending Journey raising awareness about the importance of becoming an organ by spreading the word that giving the gift of life really is the most precious gift anybody could receive."