The migrants will be given up to $3,500 (£2,600) for leaving within the next 90 days.
Israel has not clearly said where the migrants will go, but tacitly recognises it is too risky to return the Sudanese and Eritreans home.
African asylum seekers, mostly from Eritrea, who entered Israel illegally during the past years, hold placards showing migrants who they say were killed after being deported to their country, during a protest against Israel's deportation policy in front of the Supreme Court in Jerusalem on January 26, 2017.
Netanyahu said a barrier Israel completed in 2013 along its border with Egypt had effectively cut off a stream of "illegal infiltrators" from Africa after some 60,000 crossed the desert frontier.
Fleeing war and persecution, many of these migrants came from Eritrea and Sudan.
The head of the United Nations refugee agency has expressed concern about the plans.
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"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.
The order exempts children and the elderly, as well as victims of human trafficking and slavery.
Prime Minister Benjamin Netanyahu reportedly asked his security adviser on Wednesday to draw up a plan to forcibly expel undocumented asylum seekers, even as ministers approved a plan to imprison illegal migrants who refuse to leave "voluntarily".
"We have expelled about 20,000 and now the mission is to get the rest out", Mr. Netanyahu said.
African refugees who are Jewish are granted automatic asylum in Israel, as are Jews from anywhere in the world.
In August, the High Court of Justice of the Near Eastern country ruled that since deportations can only be carried out with the agreement of migrants, the refusal to leave Israel cannot be considered a non-cooperative behavior, nor be punishable by jail. Adding, an investigation by the Hotline for Refugees and Migrants, an NGO, found people who had already agreed to leave for Rwanda were vulnerable to a number of threats including imprisonment, violence and extortion. "The expulsion to Rwanda endangers the very lives of these refugees".