The Greek doctors behind the pioneering method believe it will be particularly popular with women who have put off motherhood to pursue careers.
Researcher Konstantinos Pantos, from the Genesis fertility clinic in Athens, said: "We want to be able to offer this. Whether women are in the UK, Greece, or the States, they all want to have children."
However British experts have urged caution, saying it is "dangerous" to get excited about something until there is firm proof that it works. It also raises safety and ethical concerns about the upper age limit for becoming a mother.
Older mothers face more difficult pregnancies and there are fears they could lack energy to play with a child and risk dying while it is still young.
The new technique, unveiled at the European Society of Human Reproduction and Embryology's annual conference in Helsinki this month, centres on a substance called platelet-rich plasma, or PRP.
It is made by spinning a blood sample at high speed to separate out proteins involved in tissue growth, and is already used by plastic surgeons to speed up healing.
The doctors at the Genesis clinic, which is Greece's biggest IVF unit and frequently treats British women, injected 30 women between the ages of 46 and 49 with PRP made from their own blood.
Some were still going through menopause so were having irregular periods but, in most, "everything had shut down".
After the treatment, many soon started producing eggs again - and around half made eggs that have been fertilised and are ready to use in IVF.
This includes a woman who had not had a period for five years, New Scientist reports.
All the women wanting to have children and doctors hope to start IVF in the coming months - meaning the first babies resulting from the method could be born next year.
Women usually go through the menopause around the age of 50, and all those treated had been through it early.
However, Dr Pantos says the technique may also work ten or 15 years after menopause, allowing much older women to become mothers. He said: "I see lots of women who have looked after their career and then at 43, 44, 45, say 'Let's go for a pregnancy'.
"These are career women who think success is in their grasp whatever they do. I tell them it is too late, they have gone through the menopause and they look surprised."
His colleague Konstantinos Sfakianoudis said: "It offers hope that menopausal women will be able to get pregnant using their own genetic material."
Initial work suggests the eggs to be healthy. However, much more research is needed before the technique is deemed suitable for widespread use.
Dr Pantos, who is currently only treating Greek women, stressed: "We need to be careful not to raise false hope."
Professor Allan Pacey, a Sheffield University fertility expert, said: "How to rejuvenate older ovaries is one of the holy grails of reproductive medicine.
"I have no idea how it might be working and whether it is safe, so I would urge caution.
"However, if it stands up to scrutiny, it would be quite an exciting development."
Roger Sturmey, of Hull York Medical School, said: "It is potentially quite exciting but it opens up ethical questions about what the upper age limit of mothers should be. Where would the line be drawn?"
