The migrants will be given up to $3,500 (£2,600) for leaving within the next 90 days.
They will be given the option of going to their home country or third countries.
If they do not leave, the Israeli authorities have threatened that they will start jailing them from April.
The UN refugee agency said the controversial plan violated international and Israeli laws.
The Israeli government says their return will be humane and "voluntary".
The order exempts children, elderly people, and victims of slavery and human trafficking.
People from Eritrea and Sudan make up a significant number of migrants in Israel
A spokesperson for Israel's Population and Immigration Authority told the BBC there were currently 38,000 "infiltrators" in Israel, of whom just 1,420 were being held in detention facilities.
Israel uses the term "infiltrators" to describe people who did not enter the country through an official border crossing.
Many of the migrants - who are mostly from Eritrea and Sudan - say they came to Israel to seek asylum after fleeing persecution and conflict, but the authorities regard them as economic migrants.
Israeli Prime Minister Benjamin Netanyahu has claimed that an unchecked influx of African migrants could threaten Israel's Jewish character.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. 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.