"An agreement has been reached between the two sides," said Hamas spokesman Sami Abu Zuhri.
The truce began at 19:00 local time (9:30 IST). The ceasefire announcement was greeted by celebratory gunfire on the streets of Gaza City.
Sirens warning of rockets reportedly continued to sound in southern Israel. An Israeli military spokeswoman said the army was checking whether any rockets had landed.
Cairo's initiative, Palestinians officials said, called for an indefinite halt to seven weeks of hostilities, the immediate opening of Gaza's blockaded crossings with Israel and Egypt and a widening of the enclave's fishing zone in the Mediterranean, the Jerusalem Post reported.
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Under a second stage, Israel and the Palestinians would also discuss the construction of a Gaza sea port and an Israeli release of Hamas prisoners in the West Bank, the officials said.
The Islamist Hamas movement, de facto ruler of Gaza and party to the Abbas-led efforts to agree a truce, declared victory for the resistance.
It's "a day of the victories for our people," Hamas spokesman Fawhi Barhoum declared before a cheering, screaming crowd. He praised the "steadfastness and resistance" in Gaza.
A senior Israeli government official said Israel "once again" accepted Egypt's proposed ceasefire.
Throughout the conflict, Israel has openly accepted Egypt's ceasefire proposals and slammed Hamas for not doing so.
The Israeli official said the ceasefire deal, unlike previous ones during the conflict, is unlimited in duration.
The Palestinian official said the truce deal had been finalised after 48 hours of intensive shuttle diplomacy by Azzam al-Ahmed, head of the Palestinian delegation to the protracted, on-off truce talks in Cairo.
"Over the past 48 hours, he has been shuttling between the leadership of Hamas, Islamic Jihad, all the factions, and Egyptian leaders, travelling between Ramallah, Gaza, Doha and overseas," the official said.