Mr Justice Mark Horner agreed with the Northern Ireland Human Rights Commission who had taken a case out against the region's Department of Justice (DoJ).
He told Belfast High Court: "In the circumstances, given this issue is unlikely to be grasped by the legislature in the foreseeable future, and the entitlement of citizens of Northern Ireland to have their Convention rights protected by the courts, I conclude that the Article Eight rights of women in Northern Ireland who are pregnant with fatal foetal abnormalities or who are pregnant as a result of sexual crime are breached by the impugned provisions."
Unlike other parts of the UK, the 1967 Abortion Act does not extend to Northern Ireland where abortions are banned except where the life or mental health of the mother is in danger.
Anyone who performs an illegal termination could be jailed for life.
After hearing arguments from both sides the judge ruled in favour of the Human Rights Commission and agreed that terminations should be legal in some circumstances.
The commission had claimed the current law, relating to access to termination of pregnancy services for women in cases of serious malformation of the foetus or pregnancy as a result of rape or incest, is incompatible with human rights legislation regarding inhuman and degrading treatment, privacy and discrimination.
Northern Ireland's Attorney General John Larkin, the chief legal adviser to the Stormont Assembly, was given special permission to address the court. He said there was no public appetite for a law change.
Judge Horner said without a referendum it was impossible to know how the majority of people viewed abortion and noted there was no political will to change the law.
In cases of fatal foetal abnormality (FFA), the judge concluded the mother's inability to access an abortion was a "gross interference with her personal autonomy".
He said: "In the case of an FFA there is no life to protect. When the foetus leaves the womb, it cannot survive independently. It is doomed. There is no life to protect.
"Therefore, even on a light touch review it can be said to a considerable degree of confidence that it is not proportionate to refuse to provide an exception to the criminal sanctions imposed on the impugned provisions."
The judge also claimed the current law placed a disproportionate burden on victims of sexual crime.
He said: "She has to face all the dangers and problems, emotional or otherwise, of carrying a foetus for which she bears no moral responsibility and is merely a receptacle to carry the child of a rapist and/or a person who has committed incest, or both.
"In doing so the law is enforcing prohibition of abortion against an innocent victim of a crime in a way which completely ignores the personal circumstances of the victim."
CARE in Northern Ireland spokesman Tim Houston said: "This is a deeply disappointing ruling but it is important to stress it will not result in an overnight change to the law.
"Decisions in relation to abortion law in Northern Ireland should be left in the hands of Assembly members because they are best placed to respect the wishes of people of Northern Ireland.
"Whilst recognising the traumas associated with fatal foetal abnormalities and pregnancies that result from difficult or even horrific circumstances, we do not believe abortion is the best option for the mother or the unborn child.
"At CARE we wholeheartedly support and campaign for improved pastoral and palliative care for all who have been affected by traumatic experiences leading to pregnancy or those affected by fatal foetal abnormality.
"This is what we will continue to focus on because the preservation and condition of life for both the mother and the baby is what matters most in this situation."
The NIHRC said legal proceedings had been launched as a last resort.
Speaking outside the court, Les Allamby, chief commissioner described the judgment as "historic".
He said: "We welcome today's landmark ruling.
"In taking this case we sought to change the law so that women and girls in Northern Ireland have the choice of accessing a termination of pregnancy locally in circumstances of fatal foetal abnormalities, rape or incest, without being criminalised for doing so.
"Today's result is historic, and will be welcomed by many of the vulnerable women and girls who have been faced with these situations.
"We are delighted with the result."
However, prominent pro life campaigner Bernadette Smyth expressed disappointment at the result.
She said: "We do not recognise the negative points which were made by the judge today.
"We must protect the rights of the unborn child."