Currently, abortion is only allowed when a woman’s life is at risk, but not in cases of rape, incest or fatal foetal abnormality.
The Eighth Amendment, which grants an equal right to life to the mother and unborn, will be replaced.
The declaration was made at Dublin Castle at 18:13 local time on May 25.
The only constituency to vote against repealing the Eighth amendment was Donegal, with 51.9% voting against the change.
A vote in favour of repeal paves the way for the Dáil (Irish Parliament) to legislate for change which would see the introduction of a much more liberal regime.
In 2015 the country voted overwhelmingly to legalise same-sex marriage in a historic referendum.
‘Burden of shame is gone’
Reacting to the result, the taoiseach (prime minister) Leo Varadkar, who campaigned in favour of liberalisation, said it was ‘a historic day for Ireland,’ and that a ‘quiet revolution’ had taken place.
Mr Varadkar told crowds at Dublin Castle the result showed the Irish public ‘trust and respect women to make their own decision and choices.’
He added, “It’s also a day when we say no more. No more to doctors telling their patients there’s nothing can be done for them in their own country, no more lonely journeys across the Irish Sea, no more stigma as the veil of secrecy is lifted and no more isolation as the burden of shame is gone.”
He said that some had voted yes with ‘pride’, but many had voted yes with ‘sorrowful acceptance and heavy hearts.’
Mr Varadkar said he understood that those who had voted against repeal would be unhappy.
He said he had a message for them, “I know today is not welcome and you may feel this country has taken the wrong turn, that this country is one you no longer recognise.”
“I want to reassure you that Ireland today is the same as it was last week, but more tolerant, open and respectful.”
He said by and large it had been a respectful campaign.
He added: “We voted to look reality in the eye and we did not blink.
“We choose to provide companionship where there was once a cold shoulder and medical care where we once turned a blind eye.”