The baby, named Victoria, was born in the Paris region, and is free of the disorder known as Turner Syndrome which affects both her mother and her aunt.
Karine Thiriot, 39, said she had been trying to conceive through in vitro fertilisation, for some 15 years.
"It was the first such transplant in the world between twins with Turner syndrome,", Belgian gynaecologist Jacques Donnez, who carried out the operation in August 2009, told AFP.
It was also the first ovarian transplant to be done in Europe, said Donnez, who has since successfully performed a similar operation involving sisters who are not twins.
Thiriot lacked ovaries because of Turner Syndrome, which affects one girl born in 2,500, but her twin sister, though having a similar chromosome deficiency, was fertile and had two children before the transplant.
A few months after the transplant Thiriot's regular reproductive cycle had established itself and she became pregnant quite normally.
"Victoria is totally normal and doesn't have Turner syndrome," she said.