Mr Netanyahu is fighting to stay in office after his religious-nationalist coalition lost its majority in the 27 October election.
Opposition candidate Mr Eisenkot, a former military chief, ran as the main challenger, leading a bloc of parties seeking to oust Israel’s longest-serving premier.
Neither Mr Eisenkot nor Mr Netanyahu won a clear majority in the vote, meaning a coalition will need to be formed.
A spokesperson for Mr Herzog, whose largely ceremonial role involves nominating a candidate to form a coalition after elections, said on Saturday: “President Herzog has invited Gadi Eisenkot to the President’s Residence, where he will be tasked with forming the government tomorrow.”
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