The migrants, including a five-month-old baby and four pregnant women, were rescued from their badly damaged inflatable boat on Monday by the Liberian-flagged Salamis oil tanker 80 kilometres off the Libyan coast.
In a statement released overnight, Malta said the Salamis, which had been moored off the Mediterranean island nation in international waters, was heading for Syracuse in Sicily.
"This development came as the Italian authorities accepted to welcome the migrants who are aboard the MV Salamis. It followed diplomatic contacts between the Italian, Maltese and Greek governments," the government said.
It said Prime Minister Joseph Muscat personally thanked Italian Prime Minister Enrico Letta.
"Malta's position during this crisis was always strong, consistent and legitimate. Through this position, Malta sent a strong message," Muscat was quoted as saying in the statement.
Muscat has sparked controversy with his hardline approach to boat migrants.
In July he said the government was considering expelling them, insisting he had to "get the message across that Malta is not a pushover".
The country refused to allow the 102 migrants aboard the Salamis to land despite a call from the European Commission to do so "as soon as possible" to save lives.
EU Home Affairs Commissioner Cecilia Malmström said it was Malta's "humanitarian duty" and sending the ship back "would be contrary to international law."
The Maltese government claimed that a patrolling Italian navy ship had ordered the Salamis to take the migrants to the nearest available port, in this case in Libya, but said the captain refused to obey the order.
Muscat said in a tweet on Tuesday that the country meets its international obligations but "cannot be expected to intervene in place of irresponsible boat owners who defy rules for their commercial needs."
The Salamis was heading to Malta with a consignment of oil.
Hundreds of thousands of migrants from Africa have braved the seas in dangerously ill-equipped vessels operated by traffickers to get to Italy and other parts of the European Union in recent years, many paying with their lives.
Malta had a record 880 arrivals in July with some 1,200 in total having landed on the island so far this year.
On Wednesday, Maltese police said 86 immigrants had been rescued overnight after their dinghy started taking in water, and brought to Malta.
The migrants consisted of 65 men, 17 women and four children who were dehydrated but did not need urgent medical attention, the police said.