An Israeli official, speaking on condition of anonymity, said “a complete and unlimited-in-time ceasefire” had been agreed.
Israel has also agreed to open its borders to allow humanitarian aid and building materials to be sent to Gaza, as well as the widening of Gaza’s fishing zone in the Mediterranean.
“Other issues”, such as Israel’s demand that Hamas disarms, will be dealt with at indirect, Egyptian-mediated talks “within one month from the start of the ceasefire”, according to the Egyptian govermment.
Israel and the Palestinians will also discuss the construction of a Gaza sea port and the release of Hamas prisoners in the occupied West Bank.
Palestinian President Mahmoud Abbas said the “Palestinian leadership” had agreed ” a comprehensive and permanent ceasefire” starting at 4pm GMT on Tuesday afternoon.
Israel’s offensive in Gaza was prompted by rocket fire from the strip, and sirens warning of attacks continued to sound across southern Israel after the truce was supposed to have taken effect. An Israeli military spokeswoman said the army was checking whether any rockets had landed in Israel.
Earlier, Palestinian officials said six Palestinians had died in Israeli air strikes in Gaza. Israel also bombed two tall buildings, a 13-storey apartment and office complex and 16-floor residential tower.
Israel said it had hit 15 “terror sites”, including some buildings that housed Hamas command and control centres.
Israel’s military said 70 rockets were fired from Gaza and that one damaged a house in the southern coastal town of Ashkelon, lightly wounding 10 people.
Palestinian health officials say 2,129 people – most of them civilians and including more than 490 children – have been killed in Gaza since 8 July, when Israel’s military offensive began.
Sixty-four Israeli soldiers and four civilians in Israel have also been killed.
Thousands of homes in Gaza have been destroyed or damaged in the conflict. Israel has said Hamas bears responsibility for civilian casualties because it operates among non-combatants and uses schools and mosques to store weapons and as launch sites for rockets.