A minimum of 16,250 migrants will be resettled in unspecified Western nations under the agreement announced in a statement from Prime Minister Benjamin Netanyahu's office.
Hours after announcing the deal, which was opposed by right-wingers as it would give thousands of migrants the right to stay in the country, Netanyahu posted a message on his Facebook page saying he was putting it on hold until further review.
Israel's Supreme Court had blocked deportations meant to begin on Sunday. Mr Netanyahu's office described the agreement as "unprecedented".
A group of residents of southern Tel Aviv, where numerous migrants have settled, immediately denounced the new plan in a statement, calling it "a shame for the state of Israel".
The Africans, almost all from dictatorial Eritrea and war-torn Sudan, say they fled for their lives and faced renewed danger if they returned.
As the migrants could face danger or imprisonment if returned to their homelands, Israel offered to relocate them to an unnamed African country, which deportees and aid workers said was Rwanda or Uganda.
How controversial is this issue?
Naija News recalls that the Israeli President has earlier this year announced the plan to implore illegal Africans Immigrant to leave the country voluntarily or or facing indefinite imprisonment with eventual forced expulsion.
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Some critics in the country and among the Jewish community overseas - including former ambassadors and Holocaust survivors - said the plan was unethical and a stain on Israel's global image.
Mr Netanyahu said the opposition was "baseless and absurd" and that Israel would resettle "genuine refugees". Only 10 Eritreans and one Sudanese out of over 35,000-40,000 migrants have been recognized as refugees in Israel since 2009, according to the UN.
Opposition leaders and activists in Israel hailed the new deal on Monday.
Rwanda and Uganda have said they would not accept those deported against their will.
Germany and Italy, however, said they were unaware of any such resettlement deal for African migrants from Israel, although the German interior ministry said Berlin always respected its humanitarian commitments.
But Naftali Bennett, head of the Jewish Home party that is part of Mr Netanyahu's governing coalition, condemned the plan.
The committee that came up with the plan stated that it will come up with a "rehabilitation plan" for southern Tel Aviv. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.