The breakthrough came during talks in Cairo on Monday, only days after a similar three-day truce collapsed in a deadly wave of violence within hours of starting on Friday.
The United States welcomed the three-day cessation of hostilities, adding that the onus was on the Palestinian militia to maintain the truce.
"This is a real opportunity. We strongly support the initiative," Deputy National Security Adviser Tony Blinken told CNN.
Images of the bloodshed - which has cost the lives of more than 1,800 Palestinians and 64 Israeli soldiers in and near Gaza as well as three civilians in Israel - have sent tensions in the region soaring, earning the Jewish state strong criticism.
"How many more deaths will it take to stop what must be called the carnage in Gaza?" French Foreign Minister Laurent Fabius asked, as Britain said it was reviewing licences to sell arms to Israel.
Israel and Hamas, the Islamic militant group that is the de facto ruler of Gaza, separately confirmed to AFP that they would abide by the new 72-hour ceasefire.
"Israel will be honouring the ceasefire from tomorrow (Tuesday) at 8:00am (0500 GMT)," an Israeli official said on condition of anonymity.
"Hamas informed Cairo a few minutes ago of their approval of the truce for 72 hours from tomorrow," a spokesman for the group, Sami Abu Zuhri, said.
A Palestinian delegation, including representatives of Hamas, Islamic Jihad and the Palestinian Authority, was already in Cairo for talks on the terms of an agreement between Israel and Gaza, set to take place during the three-day truce.
Abu Zuhri later said a delegation of Hamas members from Gaza would be leaving for Cairo on Tuesday to join movement leaders from Egypt and Qatar.
The Israeli official confirmed that a delegation would be arriving in Egypt to participate in the talks.
The official also accused Hamas of prolonging bloodshed by not accepting a similar Egyptian proposal three weeks ago.
Hamas had rejected that initial Egyptian proposal, saying it hadn't been consulted.
Mussa Abu Marzuk, a top figure in the Hamas politburo, said Monday that the new ceasefire proposal included an Israeli withdrawal from the Gaza Strip.
Israeli media quoted officials saying that if the truce would be upheld by Hamas, there would be no need for further military presence in Gaza.