Speaking after a landslide referendum in favour of repealing the republic's ban on abortions, Varadkar said Ireland had emerged from the shadows and come of age.
"Today is an historic day for Ireland. A quiet revolution has taken place," he said in a speech at Dublin Castle, where the referendum result was declared, showing 66 percent had voted to repeal the constitutional ban on abortions.
"We as a people have spoken. And we say that we trust women and we respect women and their decisions.
"No more doctors telling their patients there is nothing that can be done for them in their own country. No more lonely journeys across the Irish Sea.
"No more stigma. The veil of secrecy is lifted. No more isolation. The burden of shame is gone."
Varadkar, 39, was given a rock star welcome by cheering crowds packed into the castle forecourt to hear the final result of the referendum.
He said Ireland would now provide compassion and medical care for women in crisis pregnancies instead of turning a blind eye.
He told No voters feeling cut adrift that Ireland was the same country they knew, "just a little more tolerant, open and respectful".
Wrenching pain' of mistreatment
Ireland's constitution was amended in 1983 to ban abortions. Saturday's referendum result will likely see the amendment repealed before the year is out.
"This majority decision changes all that."
He said Saturday would be remembered as the day that historically deeply socially conservative Ireland "stepped out from under the last of our shadows and into the light.
"The day we came of age as a country. The day we took our place among the nations of the world."
He ended his speech saying: "The wrenching pain of decades of mistreatment of Irish women cannot be unlived. However, today we have ensured that it does not have to be lived again."
Varadkar, Ireland's first gay prime minister, came to power last year in what was seen as another major milestone for diversity in Ireland. He took over as leader of the centre-right Fine Gael party, leading a minority government.
Born to an Indian father and an Irish mother, Varadkar was a hospital doctor before becoming a family doctor in 2010.
He changed his position on abortion after hearing of two particular cases during his time as health minister from 2014 to 2016, which convinced him terminations should not be banned in the Irish constitution.
As he left Dublin Castle, he stopped for selfies and chatted with the handful of Yes-supporters still in the forecourt.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
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