The two rivals were deadlocked following last month's elections, with neither able to easily form a majority coalition, raising the possibility of an unprecedented third election in less than a year.
President Reuven Rivlin formally granted the mandate to Gantz late Wednesday, giving him 28 days to form a government. If he fails, another member of parliament could potentially assemble a majority coalition, but that scenario has never happened.
Netanyahu was given the first opportunity to form a government after assembling a large right-wing bloc, but failed to build a 61-seat majority. Gantz faces similarly steep odds, raising the possibility that Israel will hold a third election in less than a year.
Still, Gantz faces steep odds in every possible path to forming a government. He has been endorsed by just 54 lawmakers representing an array of parties that are unlikely to sit together in a coalition.
Both Gantz and Netanyahu say they favor a national unity government. Together, Netanyahu's Likud and Gantz's Blue and White control a solid 65-seat majority. But the two men are divided over who should lead any new government.
Netanyahu has insisted he head the government, at least for the first 2 years, and that it include his right-wing allies, conditions that Gantz has repeatedly rejected.
Netanyahu is likely to be indicted on corruption charges in the coming weeks, and Gantz has said Netanyahu should resolve his legal troubles before returning to the top post.
Gantz could potentially break up the right-wing alliance and recruit some of the smaller parties to his coalition. But that might be seen as a major betrayal by those parties' voters.
Another option would be to form a minority government with Avigdor Lieberman, who emerged as kingmaker after his party won eight seats and has refused to endorse either Gantz or Netanyahu. Gantz might be able to convince the Arab Joint List, which won 13 seats, to support the coalition from the outside.
That would bring down Netanyahu but result in a highly unstable government. It's also far from clear that Lieberman, a nationalist with a history of harsh rhetoric toward the Arab minority, would support such a scheme. No Arab party has ever sat in an Israeli government.
The political deadlock dates back to April, when Lieberman refused to join a right-wing coalition under Netanyahu. In response, parliament voted to dissolve itself, leading to an unprecedented repeated election in September. A similar scenario could play out again.
The political deadlock has delayed the Trump administration's release of its long-awaited peace plan. The Palestinians have already rejected the plan, accusing the administration of extreme and unfair bias toward Israel.