Doctors at the University Hospital of Wales, Cardiff, carried out the pioneering surgery three minutes after Teddy Houlston died on April 22, 2014, it was announced today.
His kidneys were used to save an adult's life in Leeds.
His father Mike Houlston, from Cardiff in Wales, told the 'Daily Mirror': "He lived and died a hero. It's impossible to explain how proud we are of him."
Teddy's mother Jess Evans was carrying twins when she was told - 12 weeks into her pregnancy - that one of the twins was fatally ill.
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Babies with the condition either die in the womb, are stillborn or live for just seconds, minutes or hours after birth.
Evans told the newspaper that the news of Teddy's condition was "soul destroying".
Though doctors offered the couple the option of an abortion, Evans said: "We thought that even if we had a moment with him, or 10 minutes, or an hour, that time was the most precious thing that we would ever experience."
As they continued with the pregnancy, the couple decided that they wanted to donate their baby's organs.
Retrieving organs from children for transplant is rare, it is particularly unusual from newborn babies - and unheard of in those with anencephaly.
Yet his kidneys would have been fully functional in the womb.
Angharad Griffiths, a specialist nurse from National Health Service's Blood and Transplant who helped complete the transplant, said she had "every belief" that a similar transplant could be successfully carried out in the future.
She said the transplant had been "challenging", particularly as they did not know if Teddy would be born alive.