The migrants were brought to shore by the Armed Forces of Malta (AFM) after they were transferred at sea from the two ships that were carrying them.
The deal also decides the future of another 249 rescued migrants already in the island nation.
Prime Minister Joseph Muscat said that the people will be re-distributed among eight European Union countries, including Ireland.
Thirty-two people were picked up off Libya on 22 December by the Dutch-registered vessel Sea Watch 3, operated by a German humanitarian group, while the Sea-Eye - a second ship run by a different German charity - rescued another 17 people on 29 December.
Malta last week allowed the boats to shelter near its coasts from the bad weather but would not let them disembark the migrants.
Another 78 will be allowed to stay in Malta, while 44 Bangladeshi migrants will be repatriated.
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Amnesty International's Southern Europe researcher Elisa De Pieri said the time taken to reach a decision on the migrants' fate was "shameful".
Sea-Watch said that the migrants finally have a "safe haven" after three weeks at sea.
Thanking civil society for its support, Sea Watch commented: "Disembarkation can not be subject to negotiations between states at the expense of people".
Italian Premier Giuseppe Conte has said that if Italy takes about 15 rescued migrant children and their parents that wouldn't "stain" the country's crackdown on accepting migrants rescued by private aid vessels.
"I am and will remain absolutely against new arrivals in Italy".
"Caving to the pressures and threats of Europe and the non-governmental organisations is a sign of weakness that Italians don't deserve".
Some 113,482 migrants crossed the Mediterranean to reach Europe past year, according to the United Nations refugee agency, which said 2,262 people lost their lives or went missing making the perilous journey.