"The fact that the result is so clear that is a more than 2-1 in favour, will make it much easier to get the legislation through the Dail (Irish lower house)", Mr Varadkar said.
Ireland's push to liberalise its laws is in contrast to another traditionally Catholic European country, Poland, where the ruling conservative party and still powerful church are seeking to ban most abortions.
The vote overturns a law which, for decades, has forced over 3,000 women to travel to Britain each year for terminations that they could not legally have in their own country.
The Justice Minister says he'd be surprised if New Zealand didn't follow Ireland's lead in abortion law reform.
Varadkar's government has promised to approve the drafting of abortion legislation at a cabinet meeting on Tuesday, May 29, and is aiming to enact the new law before the end of the year. It outlawed all abortions until 2014, when the procedure started being allowed in rare cases when a woman's life was in danger.
"The unborn child no longer has a right to life recognised by the Irish state", he said in a statement.
As per reports, thousands of Irish women travel to the United Kingdom every year for abortions or sourced abortion pills.
Britain's May refuses to relax Northern Ireland abortion rules
He said Saturday would be remembered as the day Ireland "stepped out from under the last of our shadows and into the light". Andrew Little said the result of the Irish referendum indicated that attitudes and values towards abortion were changing.
"Wonderful, wonderful, today is wonderful!" said 65-year-old Eileen Shields, who had been ostracised for falling pregnant outside of marriage when she was 18.
Campaigning ahead of Friday's referendum was often divisive and there was concern over foreign influence on Ireland's vote after revelations of meddling in the USA election.
Some supporters had tears of joy running down their cheeks, and many women hugged each other.
Katy Gaffney, a 24-year-old baker who travelled home to Dublin from Berlin to vote, stood silently in front of the makeshift memorial crying.
In a tweet following yesterday's referendum result, which showed a two-to-one Yes vote to repeal the Eighth Amendment, Dr Martin said he will pay tribute to those who "made such a huge effort to remind us that in pregnancy we are dealing with two lives - both in need of love, respect and protection".
Irish Health Minister Simon Harris said: "Under the Eighth Amendment women in crisis pregnancy have been told: 'Take the plane or take the boat.' Today we tell them: 'Take our hand'".
Mrs Yelagi also told the BBC's Swati Patil: "We are thankful to those who fought the battle for my daughter".
The anti-abortion DUP, whose 12 MPs the prime minister relies on to prop up her minority government, are against Westminster taking a decision on liberalising abortion while Stormont is suspended.
"We revealed a changed Ireland to the world and, more than that, I think we lit a beacon of hope for countries all over the world where people are working toward similar change", she said. Perhaps as a result of the stress and anticipation of the huge, important vote, people went absolutely mad when a gorgeous hound was hoisted into the air, like Simba from The Lion King.