Far-right leader Salvini was forced out of office last month after bringing the government down, and the new coalition has been trying to forge its own migrant stance.
It is the first time in 14 months that Italy has offered a migrant rescue ship a safe port, although it took Rome six days and European guarantees to redistribute the migrants before it did so.
“The Ocean Viking just received instructions from the Maritime Rescue Coordination Centre of Rome to proceed to Lampedusa,” SOS Mediterranee, which operates the vessel, tweeted.
French Interior Minister Christophe Castaner said there had been an “ad hoc” agreement to divide the migrants between five countries — Italy, France, Germany, Portugal and Luxembourg.
France and Germany have agreed to take 25 percent of the migrants each, with Italy to take 10 percent.
“We now need to agree on a genuine temporary European mechanism,” Castaner added.
The Italian coastguard will send a vessel to pick up the migrants at sea in order not to perturb port operations, Italian media reported.
Under far-right leader Salvini, charity vessels with rescued migrants on board faced fines of up to a million euros as well as the arrest of the captain and impounding of the boat.
“Having been designated a place of safety that qualifies as such is good news,” said Nicola Stalla, search and rescue coordinator aboard the Ocean Viking.
“But having to wait several days to several weeks is not tolerable,” Stalla said in a statement from SOS Mediteranee.
Salvini pulled the plug on the previous government in August in the hope of snap elections.
His move backfired and the League leader is now in opposition after previous ally the Five Star Movement and the centre-left Democratic Party agreed a coalition.
“Here we go, ports open without limits,” Salvini tweeted after the safe port announcement. “The new government is reopening the ports, Italy returns to being the refugee camp of Europe. Abusive ministers who hate Italians,” he wrote.
While Salvini spent much of his time as minister launching diatribes against migrants and rescue charities, his replacement is a civil servant and immigration expert, Luciana Lamorgese.
Italian foreign minister and M5S leader Luigi Di Maio, Salvini's former ally, told Italian television that “the safe port was assigned because the European Union agreed to our request to take most of the migrants”.
Medecins Sans Frontieres (Doctors Without Borders), which runs the ship jointly with SOS Mediterranee, said the group comprised 58 men, six women and 18 minors.
“They tell our medics their skin was burned with melted plastic and they were beaten with wooden or metal sticks,” MSF said of the migrants who departed from chaos-wracked Libya.
“Many carry psychological wounds or trauma,” MSF tweeted. Italy is trying to set up an automatic system for distributing migrants rescued in the Mediterranean between European countries, diplomatic sources
Such a deal would put an end to the case-by-case negotiations over who will take in those saved during the perilous crossing from North Africa, which has seen vulnerable asylum seekers trapped in limbo at sea for lengthy periods.
France and Germany have reportedly given their green light to the new system, which could also involve Luxembourg, Malta, Portugal, Romania and Spain.
German Interior Minister Horst Seehofer said that under the possible future agreement, Germany would take 25 percent of rescued migrants landing in Italy.
“That won't be too much for our immigration policy,” 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.
Italian Prime Minister Giuseppe Conte is expected to discuss the plan with France's President Emmanuel Macron when the latter visits Rome on Wednesday. It will then be studied in more detail at a meeting of interior ministers on September 23 in Malta, ahead of a European summit in October in Luxembourg.