Joe Quick, from Bermondsey in south-east London, is recovering in hospital after undergoing surgery last week to implant the adult kidney, which is five times the size of his own.
Doctors at Guy's Hospital said yesterday that Joe - one of the youngest patients in Britain to receive a kidney from a living donor - and his mother, Lorraine Guerrier, 33, are well.
The child has been on dialysis since his kidneys failed due to a genetic disorder when he was nine months old.
Geoff Koffman, the surgeon who carried out the transplant, said: "He is certainly the youngest living-donor transplant we have done. Joe is very small to receive an adult kidney, but it is a matter of balancing the risks.
"We wouldn't have been able to continue dialysis for much longer. He was at a desperate stage and this surgery was absolutely life saving."
He said transplants on babies are normally carried out using organs from children who have died. Joe had been on the transplant list for some time, but they had not been able to find a suitable donor.
"His mother came forward and offered to help. There are risks with any donor, but they are small. She wanted to give her son the chance of a normal life," he said.
"It will be a month or so before we can be confident that everything is fine and that he has avoided rejection, but everything is looking fine and this is a chance for him to get back to normality. He is up and about and eating, and is looking much chirpier."
Mr Koffman said the little boy's body would now have to adjust to the adult kidney. "The kidney is huge compared to him; it's like having two hearts. His body will have to adapt it to him.
"There is a risk with such a large kidney that his heart will not be able to cope with pumping all the blood into it, but we are monitoring it and he seems to be doing well."
Tests for compatibility were also carried out on Joe's father, Mark, a postman, and Joe's six-year-old sister, Charlotte.
His mother said the operation was "painful but worth it. I'm feeling a lot better and Joe has made a brilliant recovery - quicker than me. He was on his feet after just two days.
"The doctors picked me because I'm smaller than Mark, who is over six feet tall. Charlotte is too young.
"My kidney was a lot bigger than Joe's - I don't know how they fitted it in. It was a bit of a squeeze, I'm told."