"This agreement will allow for the departure from Israel of 16,250 migrants to developed countries, such as Canada, Germany and Italy," Netanyahu said.
He made the announcement in televised remarks after Israel said it had scrapped a controversial plan to deport migrants to an unnamed African country and replace it with a new one that would see thousands sent to Western countries.
Thousands of others are to remain in Israel at least temporarily.
"The agreement stipulates that for each migrant who leaves the country, we commit to give temporary residence status to another," Netanyahu said.
Netanyahu in January announced the implementation of a programme to remove migrants who entered illegally, giving them a choice between leaving voluntarily or facing indefinite imprisonment with eventual forced expulsion.
According to interior ministry figures, there are currently some 42,000 African migrants in Israel, half of them children, women or men with families, who were not facing immediate deportation.
They are mainly Sudanese and Eritrean.
As the migrants could face danger or imprisonment if returned to their homelands, Israel offered to relocate them to an unnamed African country, which deportees and aid workers said was Rwanda or Uganda.
Netanyahu said in his remarks on Monday that he had to abandon the earlier plan because the option of sending them to a third country "no longer exists".
Rwanda and Uganda have said they would not accept those deported against their will.