The migrants will be given up to $3,500 (£2,600) for leaving within the next 3 months.
The migrants 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 this year.
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, women, parents of dependent minors and victims of slavery and human trafficking.
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.