Mr Lapid, the leader of the centrist Yesh Atid party and foreign minister, will take over from Naftali Bennett under an existing power-sharing deal.
They formed an unlikely eight-party coalition after last year's election.
However it collapsed last week, clearing the way for fresh polls.
It also creates an opening for Israel's longest-serving prime minister, Benjamin Netanyahu, to return to office despite being on trial on corruption charges which he denies.