Egypt's state-affiliated Qahera TV reported the ceasefire had officially come into effect after noon in the region (8pm AEDT) on Thursday, when the enemies signed it in the Egyptian beach resort of Sharm el-Sheikh.
Israeli Prime Minister Benjamin Netanyahu's office said it would take effect only once ratified by the Israeli cabinet, which was scheduled to meet at 5pm.
Residents in Gaza reported air strikes on Gaza City about the time it was due to be signed.
Under the deal, fighting will cease, Israel will partially withdraw from Gaza and Hamas will free hostages it captured in the attack that precipitated the war, in exchange for prisoners held by Israel.
A source briefed on details said Israeli troops would begin pulling back within 24 hours of the deal being signed.
The release of all 20 Israeli hostages still believed to be alive in Gaza was expected on Sunday or Monday, an Israeli official said.
Palestinians and the families of Israeli hostages broke into wild celebrations after news emerged of the pact.
In Gaza, where most of the more than two million people have been displaced by Israeli bombing, young men applauded in the devastated streets, even as Israeli strikes continued.
"I am not the only one happy, all of the Gaza Strip is happy, all the Arab people, all of the world is happy with the ceasefire and the end of bloodshed," said Abdul Majeed Abd Rabbo in Khan Younis in southern Gaza.
Einav Zaugauker, whose son Matan is one of the last hostages, rejoiced in Tel Aviv's so-called Hostages Square, where families of those seized in the Hamas attack that sparked the war two years ago have gathered to demand their return.
"I can't breathe, I can't breathe, I can't explain what I'm feeling ... it's crazy," she said, speaking in the red glow of a celebratory flare.
Still, Gaza residents said Israeli strikes on three Gaza City suburbs continued overnight and in the morning hours of Thursday, residents said.
The Gaza health ministry said at least nine Palestinians were killed by Israeli fire in the past 24 hours.
Just a day after the second anniversary of Hamas militants' cross-border attack that triggered Israel's devastating assault on Gaza, indirect talks in Egypt yielded an agreement on the initial stage of Trump's 20-point framework.
But the agreement announced by Trump late on Wednesday was short on detail and left many unresolved questions that could yet lead to its collapse.
Still to be hammered out are plans to govern Gaza after the war, and the ultimate fate of Hamas, which has rejected Israel's demands that it give up its weapons.
Trump hailed the deal on Truth Social as "the first steps toward a Strong, Durable, and Everlasting Peace".
Israeli Prime Minister Benjamin Netanyahu called the deal "a diplomatic success and a national and moral victory for the State of Israel".
But far-right members of his coalition have long opposed any deal with Hamas, and one of them, Finance Minister Bezalel Smotrich, said Hamas must be destroyed once the hostages were returned.
The next phase of Trump's plan calls for an international body led by Trump and including former British prime minister Tony Blair to play a role in Gaza's postwar administration.
Arab countries that back the plan say it must lead to eventual independence for a Palestinian state, which Netanyahu says will never happen.
More than 67,000 Palestinians have been killed in Israel's assault on Gaza, launched after Hamas-led militants stormed through Israeli towns on October 7, 2023, killing 1200 people and capturing 251 hostages.
In parallel, Israel's military has waged campaigns that have tipped the balance of power in the Middle East, killing the leaders of Hezbollah in a campaign in Lebanon and top Iranian commanders in a 12-day war against Iran.
But global outrage has mounted against Israel's assault, leaving it internationally isolated.
Multiple rights experts, scholars and a UN inquiry say it amounts to genocide.
Israel calls its actions self-defence after the 2023 Hamas attack.
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