Donald Tusk, the European Council president, said the leaders had made a "breakthrough" that sent "a very clear message that the days of irregular migration to Europe are over".
The next step involves the presentation of the proposal to EU leaders at a key European Council meeting due to be held on March 17 and 18.
"Legal safeguards would need to govern any mechanism under which responsibility would be transferred for assessing an asylum claim," the UN High Commissioner for Refugees (UNHCR) said in a statement.
Europe's commitments to resettle refugees remained "very low compared to the needs, 20,000 places within two years on a voluntary places", it said.
Turkey is due to receive $3.3bn until the end of 2018 to cover the costs of dealing with refugees, but it reportedly asked for double the amount during Monday's talks.
Note EU-Digest: this is a good step forward - but hopefully there will also be an addendum to the treaty which reads: "cash only on delivery".