A statement late on Thursday from Interior Minister Gideon Sa'ar said Israel would soon begin a staged process of deporting the migrants, most of whom crossed the border with neighboring Egypt - Israel's frontier with Africa - since 2006.
Sa'ar said an agreement had been reached with an African country other than Eritrea and Sudan to absorb these migrants who would soon be urged "to leave of their own free will."
Michal Rozin, chairwoman of parliament's committee on foreign workers, said by telephone that Uganda was the country that had agreed to absorb migrants who had settled in Israel.
Rozin, of the left-wing Meretz party that opposes Prime Minister Benjamin Netanyahu's government, said there were "rumors" that Uganda may have agreed to the arrangement in exchange for a deal for money and weapons.
There was no immediate comment from officials in Kampala.
Without mentioning any country by name, the Haaretz newspaper said the nation where African migrants from Israel would be absorbed had recently concluded deals to be supplied with artillery guns and mortars, and to improve an aging fleet of combat aircraft.
"The government has made the agreement but the attorney general has now approved it so that it may be implemented," Rozin told Reuters by telephone.
She urged the government to expose more details of the plan, including whether there were assurances that the migrants would not be forcibly repatriated to Sudan or Eritrea, saying that in these countries "we know many would be at risk of their lives."
Human rights groups say Israel has jailed hundreds of African migrants and has taken other steps as a pressure tactic to get them to agree to leave the country.
A few thousand are believed to have left Israel in the past year since a law enacted in 2012 authorizing migrants who lack any official residence permits to be jailed for up to three years, said Sigal Rozen, policy coordinator for Hotline for Migrant Workers (HMW), an Israeli human rights group.
In July, a group of 14 Eritreans were repatriated after receiving $1,500 each from Israeli authorities, in what HMW denounced at the time as a "grave human rights violation," citing Eritrea's poor human rights record as a cause for concern.
At least one group of Africans was flown out of Israel to South Sudan in the past year and other migrants have been offered cash to leave voluntarily. Some 2,000 Africans are being held in the southern detention centers.
A fortified fence along Israel's tense border with Egypt's Sinai has largely stemmed the flow of migrants who walked across what was once a pororous frontier at a rate of up to 2,000 a month in 2011.
(Writing by Allyn Fisher-Ilan; Editing by Eric Walsh)