Fantastic crowds at Dublin Castle.
"A quiet revolution has taken place", Varadkar, who became Ireland's first openly gay prime minister past year, said in a speech after the vote.
"Today is a historic day for Ireland", Varadkar said at a press conference.
Liberal Democrat leader Sir Vince Cable has said Mrs May should take advantage of the current lack of a devolved administration and push for reform from Westminster. "And that indicates to me that we are a country that is not divided".
People over 65 voted 60 percent against. "They have said we need a modern constitution for a modern country", he said.
Officials say a final national result for Friday's referendum may not be declared until early Saturday evening.
Wogan said this time was different and held Gallagher's hand in solidarity. "You're forwarding the flag on for women". Amnesty International Ireland and the Abortion Rights Campaign, for instance, were required to return political grants of $150,000 and $25,000, respectively, to George Soros's Open Society Foundations.
"I feel enormous relief and great pride in the people of Ireland who didn't maybe know what they thought until they were finally asked the questions", Ailbhe Smyth, a longtime women's rights activist, told CNN.
With this referendum, the Catholic Church has lost its last battle in Ireland.
Dublin plans to bring in legislation this year to allow abortions with no restriction up to 12 weeks into a pregnancy, raising the prospect that women in Northern Ireland may start travelling south of the border for terminations. In Europe, only Malta and Poland have similar bans.
Former One Direction member and Irish native Niall Horan also shared his thoughts on the vote.
Siobhan Donohue, chairwoman for Termination for Medical Reasons (TFMR), an abortion rights group, said the vote is a relief for women who previously had to travel to Britain to get an abortion.
"We have voted to look reality in the eye and we did not blink".
Dr. Ruth Cullen, a spokeswoman for the anti-abortion LoveBoth campaign, conceded defeat Saturday before the count had finished. Polls had given the pro-repeal "yes" side a small lead, but suggested the contest would be close. He gave his word on this, now he must deliver on it.
Sarah Wollaston, the chair of the health select committee and a lawmaker in May's party, said she would support the proposed amendment and said Northern Ireland should at least be given a vote to decide. "Today I believe we have voted for the next generation", he said.
"While other Western nations including the United States acquiesced to the extreme abortion lobby, Ireland has been a shining beacon of hope for its strong defense of unborn children and their mothers", Dannenfelser continued, adding that "we are filled with sorrow at this outcome". But in 2012, a woman named Savita Halappanavar died in an Irish hospital after she was denied an abortion.
Among people aged 18 to 24, 87.6 percent supported the repeal, compared to 63.7 percent of people aged 50 to 64.
Senior Tory women have demanded Theresa May act to change the law on abortion in Northern Ireland after the landslide referendum in the Republic.