The High Court in Dublin decided there were no statutory or constitutional
grounds for stopping her from travelling to have the operation.
The teenager, known only as Miss D, asked the court to let her terminate the
pregnancy abroad after health chiefs had initially refused to let her go.
The girl from Leinster is four months' pregnant and doctors have told her the
foetus has not formed properly.
It suffers from anencephaly, meaning a major part of the brain, scalp and skull
is missing. If born naturally, the baby is expected to live three days at most.
Miss D has been in the care of the Health Service Executive (HSE) since March
but asked the court to step in and let her travel.
On Friday the HSE made a U-turn, saying it would not object if the teenager had
consent from a district court judge and her mother.
The mother has already said she supports her daughter's decision.
Abortion is illegal in Ireland, except when the mother's life is in danger.
It is estimated around 7,000 Irish women travel to the UK every year to
terminate their pregnancies.