Taoiseach Leo Varadaker has spoken at Dublin Castle following the declaration of results, after the referendum to appeal the 8th Amendment was passed by a margin of more than 700,000 votes.
The result was 66.4% Yes and 33.6% No.
Mr Varadkar said it was a great day for Ireland.
He said: "A quiet revolution has taken place and a great act of democracy, 100 years since women got the right to vote.
"Today, we as a people have spoken. And we say that we trust women and we respect women and their decisions."
He continued: "For me it is also the day when we said No More.
"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."
Mr Varadkar said that this "resounding result"' gives his Government a mandate to "bring forward legislation and secure its passage by the end of the year".
He spoke to reassure those who voted No, saying: "I know today is not welcome (for you).
"You may feel that the country has taken the wrong turn, is no longer a country you recognise.
"I would like to reassure you that Ireland is still the same country today as it was before, just a little more tolerant, open and respectful."
Going forward, Mr Varadkar said the he wants Ireland to become a "better place to raise a family."
"We all want to ensure that there are fewer crisis pregnancies and fewer abortions.
"Thanks to sex education, wider availability of contraceptives and emergency contraception, abortion rates are already falling and teenage pregnancy is at its lowest since the 1960s.
"We will continue to improve access to sexual health and education to reduce crisis pregnancies and abortions further in the year ahead."
Meanwhile, Doctors for Choice have also welcomed the overwhelming Yes result.
Co-founder and spokesperson for DfC Dr Mary Favier said: “After years of witnessing the harms of the Eighth Amendment and campaigning to have it removed, we are delighted to see this momentous result for Ireland and Irish women.
"A Yes result may go some way to repair the hurt and suffering the Eighth Amendment has caused for the estimated 170,000 Irish women and girls that have had to travel for abortions since 1980, and the uncountable number who have taken illegal medication abortion pills bought online; women who the state abandoned: legally, morally and when they most needed healthcare.”
Dr Marion Dyer, spokesperson for DfC continued: “Doctors will continue to care for and support all pregnant women in their surgeries and clinics – whatever their circumstances and whatever their decisions. DfC will also continue to advocate for them. More than 1,642 doctors have declared their respect and support for pregnant women and their decisions. Ireland has voted to care for all pregnant women equally.”
The Irish College of General Practitioners has welcomed the "clarity" brought by the referendum outcome, and said it must be accompanied by other measures to minimise crisis pregnancies, including comprehensive contraceptive services and sexual health education programmes.
In a statement, the College said: "More detailed information will need to be gathered to inform legislators, and to enable the Department of Health, together with the post-graduate training bodies and the representative bodies, to comprehensively draw up the detail and resourcing of services for those with crisis pregnancies."
Meanwhile, The Irish Human Rights and Equality Commission also welcomed the referendum result. Chief Commissioner of the Irish Human Rights and Equality Commission Emily Logan said: "Today’s emphatic vote to repeal the Eighth Amendment paves the way for the development of a new legislative and regulatory framework for access to abortion services in Ireland.
"Ireland has an obligation, under international human rights law, to vindicate the human rights of women and girls in accessing healthcare that is safe, appropriate and respects their right to privacy. The Oireachtas now has an obligation to legislate to make those rights a reality.”