The influx largely stopped when Israel completed building a high-tech fence along its 150-mile border with Egypt in 2013.
The migrants will be given up to $3,500 (£2,600) for leaving within the next 90 days.
It was gathered that the Israeli authorities have threatened to start jailing them from April if they do not leave.
An immigration official, speaking on condition of anonymity, said there are some 38,000 migrants living illegally in Israel, and some 1,420 are being held in two detention centres.
Those who leave by the end of March will be given $3500 (R43 200), along with airfare and other incentives.
"Every country must maintain its borders, and protecting the borders from illegal infiltration is both a right and a basic duty of a sovereign state", he added.
"We know from numerous testimonies that the refugees who are sent to Rwanda are tortured and not given any security, status or work permits, so they must continue with their asylum journey", she said.
Human trafficking and slave victims, the elderly and children have been excluded from this order.
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Netanyahu, who has in the past blamed migrants as posing a threat to Israel's social fabric and Jewish character, on Wednesday moved to reassure Israeli residents in the poorer neighbourhoods of Tel Aviv where migrants live that there would be a return to safety and security.
"We have expelled about 20,000 and now the mission is to get the rest out", Mr. Netanyahu said. The ultimatum is part of a large-scale campaign to remove 42,000 illegal African migrants from Israel.
Those who don't voluntarily cooperate will end up staying as guests of the Holot Prison facility until they are deported.
Israel has granted asylum to some people who have applied in the past.
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Then, in the aftermath of the cabinet meeting that discussed the fate of the African migrants, Israel's parliament gave preliminary approval to a bill making it easier for "terrorists" to be sentenced to death after Netanyahu said it was necessary in extreme cases. The government now considers most of the "infiltrators" to be economic migrants.
The Center for Refugees and Migrants, Amnesty International Israel, the Association for Civil Rights in Israel and other groups signed a letter calling for the expulsions to be stopped. After spending years in Israel in dire conditions, 12 Eritrean migrants decided to make the journey to Rwanda.
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