The first-born boy weighed 6lb 11oz, while his sister weighed 5lb 14oz.
In the process, women need not take potentially risky fertility drugs like with IVF.
For standard IVF treatment, a woman is given drugs to shut down ovaries, followed by two weeks of daily hormone injections that mature eggs.
With IVM, the woman needs is given just one injection. The immature eggs are obtained from a woman's unstimulated ovaries through ultrasound guidance and then developed in the laboratory for 1-2 days.
Under IVM, the mother gave birth to the twins with the help of her own eggs developed in a laboratory.
Though the technique is also cheaper and faster, its success rate is lower.
"This is good news. There is always a need for alternative ways of doing things," the BBC quoted Dr Richard Fleming, of the British Fertility Society, as saying.
Tim Child, consultant gynaecologist at the Oxford Fertility Clinic says IVM has advantages over IVF for some women, especially with polycystic ovarian syndrome.
IVM also cuts the risk of a condition called ovarian hyperstimulation syndrome (OHSS).
"IVF, overall, has a better success rate, but the side effects are higher," Child said.
"Patients should have the choice of an alternative. IVM is safer, simpler, cheaper and more acceptable."
"This is good news. There is always a need for alternative ways of doing things," Dr Richard Fleming, of the Glasgow Centre for Reproductive Medicine and the British Fertility Society, said.