Eighty-two migrants have disembarked on the southern Italian island of Lampedusa after six days at sea.
Italy says it is allowing the ship, the Ocean Viking, to offload the migrants as most of those on board will be relocated to other EU countries.
The move signals a change of approach to migration from the new coalition which took office on Tuesday.
Ex-Interior Minister Matteo Salvini routinely blocked access to charity-run migrant vessels.
The migrants were transferred from the Ocean Viking to a coastguard vessel before being taken ashore, Italian TV pictures showed.
Italian Foreign Minister Luigi Di Maio told Italian television that "the safe port was assigned because the European Union agreed to our request to take most of the migrants".
But this did not mark a return to a policy of open ports, he added.
"It must be clear that, even in the past with the previous government, our goal was to ensure that those migrants who arrived in Italy were redistributed to other European countries."
Mr Salvini, the leader of the far-right League and former ally of Mr Di Maio's, pulled out of the coalition with his Five Star party last month in a bid to trigger new elections.
French Interior Minister Christophe Castaner tweeted on Saturday that an ad hoc European agreement had been reached between Italy, France, Germany, Portugal and Luxembourg to allow the landing. "We now need to agree on a genuine temporary European mechanism," he added.
The EU appears to be inching towards a mechanism for this - even if it is initially a temporary, partial one.
German Interior Minister Horst Seehofer said that under the possible future agreement, his country would take 25% of rescued migrants landing in Italy. "That won't be too much for our immigration policy," Mr Seehofer told Saturday's Sueddeutsche Zeitung daily.
He said it was time to end the "painful process" of haggling over each boatload of rescued migrants.
EU interior ministers will meet in Malta later this month to try to reach a wider deal, ahead of a European summit in October in Luxembourg.
France and Germany have each agreed to take a quarter of the boat's migrants, with Italy to take 10%, AFP news agency reports.
SOS Méditerranée is running the rescue ship jointly with Médecins Sans Frontières (MSF).
It said on Twitter it had received the green light to sail to Lampedusa, six days after it carried out the migrant rescue off the coast of Libya.
MSF said the group comprised 58 men, six women and 18 minors.
Earlier, they tweeted the reaction of the migrants on board when they were told they had been allowed to disembark in Italy.
🔴The moment 82 rescued men, women and children onboard the #OceanViking heard they had finally been granted a place of safety and are on their way to the island of #Lampedusa in #Italy pic.twitter.com/myBY1ZJotp— MSF Sea (@MSF_Sea) September 14, 2019
In recent years Italy, like Greece, has struggled to cope with migrant boats sailing from North Africa or Turkey.
People-smuggling gangs continue to make huge profits from African migrants desperate to reach Europe, as they flee war or poverty.
Libya is a major transit hub, but it is chaotic and violence is rife.