A new abortion law will be in place by the end of the year, Irish Prime Minister Leo Varadkar has said.
It follows a landslide vote in favour of repealing the Republic of Ireland's constitutional ban on abortion.
The proposed legislation will allow abortions during the first 12 weeks of pregnancy, and up to the 24th week in exceptional circumstances.
Irish Minister for Health Simon Harris will seek the cabinet's backing on Tuesday to draft the new legislation.
Seismic shift for Ireland
Timeline: Ireland and abortion
The result south of the border has shifted focus to Northern Ireland's similarly strict abortion laws, with UK Prime Minister Theresa May facing calls to act.
Northern Ireland will soon become the only part of the UK and Ireland with an almost blanket ban on terminations.
But Mrs May is in a difficult situation because her administration depends on the support of 10 Democratic Unionist Party MPs - who strongly oppose any reform.
On Saturday, Penny Mordaunt - who is responsible for the women and equalities brief in government - said the referendum signalled a "historic and great day for Ireland" and a "hopeful one for Northern Ireland".
Nicky Morgan and three other former holders of the women and equalities role - Amber Rudd, Justine Greening and Maria Miller - all back Ms Mordaunt's support for liberalising the laws in Northern Ireland, the Sunday Times reported.
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.
"The position in Northern Ireland is now highly anomalous and I think, probably, action will now have to be taken," he said.
At Dublin Castle on Saturday, Sinn Féin leader Mary Lou McDonald and her deputy Michelle O'Neill held up a sign saying "The north is next".