The 8th Amendment effectively bans abortions, and now, terminations are only allowed when a woman's life is at risk.
The referendum was the result of a decades-long debate about abortion in the Republic of Ireland and was the country's sixth vote on the issue.
Unsurprisingly, young people were overwhelmingly in favour of repealing the amendment, with 87 percent of voters aged 18-24 casting their ballot for reform.
Mr O'Gorman said the findings of the exit polls, which shows the yes vote was consistent across rural and urban areas, is not a shock to him.
A voter arrives at a polling station in Dublin.
All paper ballots must be counted and tallied for the official vote, as the exit polls are merely predictions.
Results for different parts of the country are expected from 1100 GMT, with a final result to be announced later in the day at the main counting centre in Dublin Castle.
Although the point at which a pregnancy is considered "viable" - that is, that the baby could potentially survive outside the womb - differs from country to country, it's most often put at 21-23 weeks, making the likelihood that Halappanavar's foetus, at just 17 weeks, would have survived birth at the point that doctors were fruitlessly attempting to save it near zero.
As Ireland votes to repeal a constitutional ban on abortions, one group believes Canadians take reproductive rights for granted. However, the Catholic Church's influence has waned in recent years following a series of child sex abuse scandals.
She was a successful dentist who lived with her husband Praveen in Galway, on the west coast of the Republic of Ireland - one of the most breathtakingly attractive parts of the world.
The Together For Yes organisation said: "This is a vote for dignity and decency".
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"I'm a staunch No".
She said her vote would be one for solidarity and compassion, "a vote to say, I don't send you away anymore".
Dublin voter Helen, 47, who did not want to give her surname and is now unemployed after suffering cancer, said her radiation treatment would have been stopped had she been pregnant, under existing laws giving equal right to life to expectant mothers and unborn babies.
Canvassers were out on the city's streets holding up signs and wearing t-shirts with campaign slogans.
Although polls had predicted victory for the Yes side, few anticipated the great wave of support for repeal of Eighth Amendment that swept the country.
Vera Rooney voted against repeal.
Anyone terminating a pregnancy in Ireland could face 14 years in jail.
Three years on, the country yesterday (May 25) headed to the polls again, in a bid to overturn a law restricting access to abortion in the country.
People Before Profit TD BrÍd Smith said the referendum is a game changer and we will never go back to the "dark days" of denial of women's rights.
Since 2013, terminations have only been allowed in Ireland when the life of the mother is at risk, including from suicide.
If a majority has voted yes - as appears to be the case - then the Irish government's recommendation is that women will be able to access a termination within the first 12 weeks of their pregnancy.