The agreement comes after Netanyahu's right-wing alliance won a comfortable victory in this month's parliamentary election, Israel's fifth in less than four years.
Netanyahu is still continuing talks with three other parties on forming the new government.
"We took a big step [last night] towards a full coalition agreement, toward forming a fully, fully right-wing government," Mr Ben-Gvir, leader of the Jewish Power party, said in a statement.
Far-right Ben-Gvir, who was convicted in 2007 of racist incitement against Arabs and backing a group considered by Israel and the United States to be a terrorist organisation, will have an expanded security portfolio that will include responsibility for border police in the occupied West Bank.
The Palestinian Authority's Foreign Affairs Ministry said the appointment would have a "potentially catastrophic impact on the Israeli-Palestinian conflict" and hinder the revival of negotiations between the two sides.
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