The truce, ending seven weeks of fighting that has left more than 2,200 people – mostly Palestinians – dead, was brokered by Egypt and began at 19:00 local time.
Hamas said the deal represented a “victory for the resistance”.
Israel is to ease its blockade of Gaza to allow in aid and building materials, Israeli officials said.
Indirect talks on more contentious issues, including Israel’s call for militant groups in Gaza to disarm, will begin in Cairo within a month.
The US gave the full backing to the deal, with State Department spokeswoman Jen Psaki saying: “We strongly support the ceasefire announcement.”
UN Secretary General Ban Ki-moon also welcomed the truce. But in a statement via his spokesman, Ban Ki-moon warned that “any peace effort that does not tackle the root causes of the crisis will do little more than set the stage for the next cycle of violence”.
The breakthrough came as both Israel and the Palestinians continued to trade fire.
A last-minute volley of mortar shells from Gaza killed an Israeli civilian and wounded six others in Eshkol Regional Council.
Earlier on Tuesday, at least six Palestinians were killed in a series of Israeli air strikes in Gaza, Palestinian officials said.
Palestinian officials said Egypt’s cease fire proposal called for an indefinite end to hostilities, the immediate opening of Gaza’s crossings with Israel and Egypt, and an extension of the territory’s Mediterranean fishing zone.
A month later Israel and the Palestinian factions would discuss the construction of a seaport and airport in Gaza and the freeing of about 100 prisoners.
Israel and Egypt were also said to be demanding guarantees that weapons would not be smuggled into Gaza.
The announcement was greeted by celebratory gunfire on the streets of Gaza City.
However, sirens warning of rockets reportedly continued to sound in southern Israel.
A spokesman for Hamas, which controls Gaza, said: “We are here today to declare the victory of the resistance, the victory of Gaza, with the help of God, and the steadfastness of our people and the noble resistance.”
Israel launched Operation Protective Edge on July 8 with the stated aim of ending rocket fire. It was later expanded to include the destruction of tunnels used by militants for cross-border attacks.
At least 2,140 people, most of them civilians, have been killed in Gaza, according to the Palestinian health ministry.
The Israeli authorities say 64 Israeli soldiers have been killed, along with three Israeli civilians and a Thai national.
Early on Tuesday, Israeli jets bombed two high-rise buildings in Gaza City, containing flats and offices.
No-one was reported killed as residents managed to flee both buildings after the Israeli military warned them to leave.
Hamas, citing Palestinian casualties, has accused Israel of an “unprecedented act of revenge” against civilians.
However, Israeli military spokesman Lt Col Peter Lerner told the Associated Press the strikes were “a direct result of Hamas’ decision to situate their terrorist infrastructure within the civilian sphere, including schools, hospitals and high-rise buildings”.
aCmgFRdofXsThe US House Ethics Committee has voted to release its report on former Republican Representative…
ABC News has agreed to pay $15 million to President-elect Donald Trump to settle a…
South Korea’s parliament has voted to impeach President Yoon Suk Yeol over his failed attempt…
Israeli war planes have carried out more than 100 air strikes in Syria on December…
President-elect Donald Trump has threatened to impose 100% tariffs on the BRICS countries if they…
Syrian troops have withdrawn from the city of Aleppo following an offensive by rebels opposed…