The migrants have been stranded off the coast of Malta on two boats since late previous year, with some suffering from dehydration and seasickness.
The agreement calls for 131 to be relocated to other European Union nations, 74 to remain in Malta and to have European Union experts review the circumstances of 44 migrants from Bangladesh before their destinations are decided.
In the meantime, those aboard the Sea Watch and Sea Eye - who include a baby and several children - were celebrating the end of 19 days at sea.
The Maltese Prime Minister, Joseph Muscat, according to information published here, specified that the people will be picked up by a military ship, from where they will be transshipped and redistributed to the eight European Union nations mentioned.
"It is a testament to state failure; politics should never be played at the cost of people in need.""Every hour that passed without a solution was not an hour I was proud of", he said.
"We welcome this show of solidarity and understanding that Malta is going beyond what is required of us", said Mr Muscat.
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"We want to express our gratitude to. all cities, federal states and provinces that declared their ports open and their willingness to welcome people".
"I reiterate, as I did before, that this case shall not act as a precedent - and I have reassurances that this will not be the case from European institutions".
Seventeen people on board another ship and 249 rescued migrants already in Malta will also be divided up between the eight countries as part of the deal, Malta said.
"The government won't fall, but I will be asking for immediate clarification in the coming hours, as soon as I get back to Italy", he said.
Salvini, who is also interior minister, leads the right-wing, anti-migrant League, one of two coalition parties in Italy's populist government.
"To give in to the pressures and the threats of Europe and NGOs is a signal of weakness that Italians don't deserve", he added, a possible jab at Conte and the leader of the 5-Star Movement.
Some 113,482 migrants crossed the Mediterranean to reach Europe previous year, according to the United Nations refugee agency, which said 2,262 people lost their lives or went missing making the perilous journey.