Netanyahu's office announced today that he had tested negative for coronavirus.
The political wrangling comes at a sensitive time.
The final go-ahead also came the day a new Israeli legislature was sworn in following the country's third election in less than a year - meaning it bypassed the typically required oversight of a special parliamentary subcommittee that had already begun reviewing the measures.
After consultations with all the parties elected to the Knesset on March 2, Rivlin heard 61 recommendations for Gantz as prime minister-33 from his own Blue and White Party, six from Labor/Meretz, seven from Avigdor Lieberman's Yisrael Beiteinu and an unprecedented 15 from the Joint Arab List.
He will now have a month to cobble together a governing coalition. One lawmaker refused to endorse either side.
Facing a hard decision, Mr Rivlin had earlier implored for a power-sharing unity deal. Gantz promised to "do whatever it takes to form within as few days as possible a national, patriotic and broad government". Israel's largely ceremonial president Reuven Rivlin will preside over the unusual event after the Israeli Knesset, or parliament, was thoroughly sprayed with disinfectant.
Gantz will face a hard task securing a governing coalition. Now, coronavirus could finally give the country its first government in more than a year.
Aside from being anti-Netanyahu, the Joint List and Yisrael Beiteinu have nearly no common political ground.
By drawing in a clandestine security agency to deal with a civilian health crisis, she said, "Israel is not aligning itself with the democracies".
During the transition period, his Blue and White party is expected to name one of its members as speaker of the parliament.
The message to Netanyahu is that the opposition now has the power to push him towards compromises during the negotiations, or remove him from power. Even now, Netanyahu and his henchmen, chief among them Culture Minister Miri Regev, continue to fuel the fires of incitement against the politicians representing Arab voters, plus some 20,000 Jewish ones, calling them "terror supporters".
Both the leaders discussed the possibility of setting up a coalition government given the current situation of the pandemic.
Gantz hoped to be able to arm a minority government with the external support of the Arab parties.
Last week, the Israeli Central Court in East Jerusalem had rejected Netanyahu's request to delay his trial.
Charges against him include bribery, breach of trust and fraud.
His trial had been due to open on Tuesday, but Jerusalem's District Court said that given the severity of the coronavirus crisis it had been instructed to hear "only urgent matters".
The premier is accused of a range of offences including receiving improper gifts and offering a media mogul lucrative regulatory changes in exchange for favourable coverage. The long-ruling Israeli leader denies any wrongdoing and says he is the victim of a media-orchestrated witch hunt.
Much of the country ground to a standstill Sunday, with schools, malls and places of entertainment shut down.
More than 127,000 people in more than 110 countries have been infected. In Israel, some 200 people have been infected with no casualties yet, as severe measures seem to have proven effective so far.
For most people, the coronavirus causes only mild or moderate symptoms, such as fever and cough.
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