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But their deal was challenged by nongovernmental organizations, other political parties and advocacy groups who argued Mr. Netanyahu shouldn’t be leading a government while he faces bribery, fraud and breach of trust charges.

Late on Wednesday, the panel of 11 High Court judges decided not to intervene. “The legal decision we’ve reached is not meant to detract from the seriousness of the pending charges against MP Benjamin Netanyahu…nor from the difficulty of the tenure of a prime minister charged with criminal acts,” the justices wrote in their decision. “It is the result…of having the presumption of innocence.”

Mr. Netanyahu, the first sitting premier to be indicted, will go on trial on May 24. He denies wrongdoing.

Messrs. Netanyahu and Gantz said Wednesday that the new government will be sworn in on May 13. It is expected to be the largest in Israel’s history in terms of ministers and deputy ministers.

Under the terms of the unity deal, Mr. Netanyahu will serve first as prime minister and Mr. Gantz will assume the position in 2021. The agreement is a complicated contract aimed at incentivizing both sides to stick with the deal amid deep mistrust.

Israel’s parliament is expected to finish voting on legislation enshrining the coalition agreement overnight, according to the two leaders’ parties, and on Thursday is expected to vote to give Mr. Netanyahu the mandate to form the next government before a midnight deadline. If he doesn’t receive the mandate by then, Israel would go to a fourth election.

Following criticism of the deal from the High Court during the hearings this week, Mr. Netanyahu’s Likud party and Mr. Gantz’s Blue and White amended the original agreement, saying they won’t allow an emergency period designed to handle the coronavirus to last longer than six months. The coalition will allow laws not related to the pandemic to pass during that time, though coronavirus legislation will have priority.

They had previously agreed that the new government would prioritize legislation to annex parts of the West Bank agreed upon with the U.S. government starting on July 1. American officials said they are prepared to recognize Israel’s sovereignty in the agreed-upon areas.

Mr. Gantz, a former military chief, last year formed the Blue and White party as a broad coalition aimed at unseating Mr. Netanyahu, but he splintered the alliance and joined the premier as the deadlock persisted and Israel began to take sweeping measures to confront the coronavirus.

While the court paved the way for Mr. Netanyahu to remain in power, it said that the coalition agreement could face legal challenges in the future, including on whether Mr. Netanyahu would be able to serve as the deputy prime minister once Mr. Gantz becomes prime minister. Ministers aren’t allowed to serve under indictment.

Politicians from center and left-wing parties criticized Mr. Netanyahu’s willingness to serve while charged, which was a key issue during the three election campaigns over the past year.

“Even if it’s legal for someone indicted on bribery charges to form a government, it doesn’t make it stink any less,” said Tamar Zandberg, a member of the Meretz party.

Meanwhile, Mr. Netanyahu’s allies hailed the decision and said it upheld the will of Israeli voters.

“The judges in Jerusalem acted well not to intervene. There is a sovereign in Israel—the nation, and it has spoken,” said Miri Regev, the culture minister and a member of Mr. Netanyahu’s Likud party.

Mr. Netanyahu withdrew an earlier request for immunity from trial after he failed to marshal enough support for it in the Knesset, the nation’s parliament. But as prime minister, his trial would be heard by an expanded panel of judges in a Jerusalem court, and he could be poised to receive a better plea deal should he choose to go that route, though he has said he won’t seek a plea deal.

—Dov Lieber contributed to this article.