Susanne Butscher, 39, was given the ovary by her twin sister Dorothee a year ago after she suffered an early menopause.
She named her daughter Maja after the Roman goddess of fertility and hopes her story will offer hope to other women, she told the Daily Telegraph.
"Being the first woman in the world to give birth after a whole ovary transplant hasn't sunk in yet, but I'm just so grateful to the doctors who enabled this to happen and to my sister, of course.
"I'm so lucky to have had this wonderful opportunity, which has given me a sense of completeness I would never have had otherwise.
"When I saw her for the first time I just cried. She really is a little miracle."
Mrs Butscher, who is German, gave birth Maja, who weighed 7lb 15oz, in London's Portland Hospital on Tuesday.
The acupuncturist and complementary therapist told the newspaper she was diagnosed as being infertile 12 years ago and was told her ovaries were not working properly.
Mrs Butscher and her husband Stephan, 40, moved to London six years ago.
Dr Sherman Silber, who carried out the ovary transplant operation, is based at the Infertility Centre of St Louis in the United States.
He has given ovarian tissue transplants to nine twins previously but Mrs Butscher's case is the first successful whole ovary transplant.
After the transplant, she began ovulating naturally for the first time, she told the newspaper.
Her twin sister has two children and lives in British Columbia.