The grieving 60-year-old begged the Court of Appeal to help her to fulfil the last wishes of her "much-loved and only child", who lost a battle with bowel cancer in 2011.
The landmark ruling - believed to be the first in British history - allows the grandmother to travel overseas and use a sperm donor.
And it overturns an earlier High Court decision to dismiss the case.
Lawyers for the woman and her husband, referred to only as Mr and Mrs M, told how the eggs would be allowed to "perish" if they were not allowed to carry out their daughter's desperate last wish.
She "never wavered" in her desire to become a mum and asked her own mother to help when she learned her cancer was untreatable.
Today Sir James Munby, Lady Justice Arden and Lord Justice Burnett allowed the appeal and remitted the case to the Human Fertilisation and Embryology Authority (HFEA) for further consideration.Mr and Mrs M were not in court for the ruling.
The (HFEA) - which regulates fertility in the UK said in 2014 that the daughter's eggs could not be harvested because she had not given her full written consent.
But, in the latest legal proceedings, lawyers acting for the mother told the judges she wanted to fulfil her daughter's wishes to carry a child created from her frozen eggs and "raise that child".
The daughter's eggs - which she referred to as her babies - were harvested and stored at a fertility centre in west London during her cancer battle amid fears she would treatment would leave her infertile.
Referred to simply as A for legal reasons, the daughter revealed her deep desire to become a parent when she realised she was dying.She told her mother: ‘I want you to carry my babies... I want you and Dad to bring them up, they will be safe with you.’
The HEFA also expressed concerns that the daughter didn't realise her mother's health could be at risk by becoming carrying a child.
But doctors said Mrs M’s age meant her chances of carrying a child were small.
Although she had a greater risk of suffering complications it was ‘likely’ she could give birth safely, the court heard.In the earlier High Court hearing, Mr Justice Ouseley ruled that the HFEA had been entitled to find the daughter had not given 'the required consent'.
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