Home affairs ministers from the 27-member bloc sealed the deal, hoping to end years of division dating back to 2015 when more than a million people - mostly fleeing war in Syria - reached the EU across the Mediterranean.
Germany's Nancy Faeser hailed the agreement as "historic".
The bloc's top migration official said it amounted to "a win-win" situation for all EU member states.
"This is a great, great achievement, showing that it's possible to work together on migration. We are so much stronger when we work together," home affairs commissioner Ylva Johansson said.
Hosting immigrants has become an increasingly divisive issue in the bloc since 2015.
Unable to agree how to share the responsibility, EU countries mostly focused on bringing down arrivals, with United Nations data showing fewer than 160,000 people made it across the sea last year to the bloc of half a billion people.
Nearly 2500 people died or went missing in the dangerous crossing over the same period.
Countries on the EU's southern edge, including Italy and Greece, have long demanded more help to cope with the numbers of people arriving on their shores.
Richer countries, including Germany and Sweden, have baulked at how many head on to their soil.
Eastern EU countries such as Poland and Hungary refused to host anyone from the mainly-Muslim Middle East and North Africa while populist parties across the bloc have fuelled the debate with anti-immigration rhetoric.
"You can still win and lose any election in any member state on migration. It is an illustration of how contentious this issue is," said an EU diplomat involved in the negotiations.
As the ministers talked, Italian Prime Minister Giorgia Meloni, her Dutch peer Mark Rutte and the head of EU executive announced a visit to Tunisia to discuss economic and energy ties with the country, a gateway for African migration to Europe.
Earlier on Thursday, Italy and Greece demanded last-minute changes to the proposed agreement, pushing for a cut in the number of people each state would take on and laxer rules to send people back to countries outside of the EU.
Under the deal that eventually came together and is to be finalised ahead of a 2024 EU election, each country would be responsible for a set number of people but would not necessarily have to take them in.
Countries unwilling to receive irregular migrants and refugees arriving ad hoc to the EU would be able to help their hosting peers through cash - about 20,000 euros ($A32,100) per person - equipment or personnel.
The agreement would introduce a new expedited border procedure for those deemed unlikely to win asylum to prevent them from lingering inside the bloc for years.
Poland and Hungary - among the EU's loudest voices against accepting sea immigrants - opposed the deal, saying the bloc's leaders should return to the matter when they meet later in June.
That, however, did not scupper the majority deal.
Liberal critics of the agreement said the rapid border procedure risked reviving tragic scenes that played out on the Greek islands several years ago by creating even more overcrowded and inadequate migration camps on EU periphery.
