Ireland is to accept migrants to Europe as part of "burden sharing" measures agreed with other EU leaders.
Discussions in Brussels concluded at 5am and were delayed after Italy's new Prime Minister Giuseppe Conte refused to sign off conclusions until he received assurances.
Taoiseach Leo Varadkar said: "We took the view that we needed to have a degree of burden-sharing, on the transfer of migrants to countries, and Ireland has already agreed to accept some from that as well."
Minister for Foreign Affairs Simon Coveney previously said the Republic had committed to take 10% of the number of migrants on board the MV Lifeline, which was stranded for days in the Mediterranean.
Mr Varadkar took part in overnight discussions on the migration issue with his EU counterparts at the European Council.
Migrant centres are to be established in EU states to process asylum claims after all-night talks hammered out a compromise package of measures.
Italy's new populist government closed ports to rescue ships operated by charities, calling on its EU partners to share the burden of looking after those saved off Libya's coastline.
Mr Varadkar added: "The 28 members agreed a compromise framework on managing migration largely based on the principle that this is a European problem and one that we need to work together on.
"We committed to working with African countries, supporting them to build up governance, to build up security and economic opportunity, providing an extra 500 million (euro) (£443 million) to the European Trust Fund for Africa."
The leaders said they would also consider "disembarkation platforms", centres in north Africa for rescued refugees.
The Taoiseach has previously called for border security to be stepped up in response to the growing challenges posed by migrants crossing from Africa to Italy.
He has urged zero-tolerance of human trafficking.
The Irish Defence Forces LE Samuel Beckett patrol vessel was deployed on the EU's Operation Sophia in the Mediterranean earlier this year.
Mr Varadkar has said reception centres for migrants should be run by the UN High Commissioner for Refugees (UNHCR) and warned there could be no equivocation over trafficking.
The Irish rescue effort is in support of the EU's work and is part of a 27-nation mission operating mainly between Libya and Italy.