German Chancellor Angela Merkel had warned that the bloc's "destiny" was at stake if it failed to reach an agreement, with her own job also hanging in the balance as tensions over the issue grow at home.
Italian Prime Minister Giuseppe Conte, who heads a month-old populist and anti-immigration government, had vetoed joint conclusions for the entire agenda of the summit in Brussels until his demands were met.
Italy has recently refused to let several migrant rescue boats dock at its ports, demanding that the responsibility for people arriving across the Mediterranean should be shared between other countries.
Twelve hours after talks began, EU President Donald Tusk said on Twitter that "EU28 leaders have agreed on... conclusions" including migration.
French President Emmanuel Macron said that "European cooperation enabled this".
Italy's stance has revived political tensions in the EU, despite the fact that arrivals have dipped sharply since Europe's migration crisis erupted in 2015, and sparked warnings that authoritarian movements will take advantage of any failure to tackle migration.
Former law professor Conte, until recently a virtual political unknown, came to Brussels emboldened by the announcement of an upcoming visit to US President Donald Trump, who has hailed Rome's tough stance, and who himself blocked the conclusions of a recent G7 leaders meeting on trade.
"Italy does not need more words, but concrete actions," Conte told reporters as he arrived at the summit.
The Italian government wants other countries to help in the same way that they had after it refused to admit the rescue ships Aquarius, which docked later in Spain, and Lifeline, which went to Malta.