An Israeli military spokeswoman declined to comment on the deal, but there appeared to have been no rocket fire or Israeli strikes after it was due to take effect, an AFP correspondent in Gaza said.
Egypt brokered the agreement to cease hostilities from 4:30 am (0130 GMT), an official from the strip's Islamist rulers Hamas and another from its allied group Islamic Jihad said on condition of anonymity.
An Egyptian official also confirmed the deal on condition of anonymity.
The deal came after the most serious flare-up in violence between Israel and Palestinian militants in Gaza since a 2014 war.
The escalation began Saturday with massive rocket fire from Gaza, drawing waves of Israeli retaliatory strikes, and continued throughout Sunday.
At least 23 Palestinians, including at least nine militants, were killed.
Four civilians in Israel were killed, at least three of them Israeli citizens.
The flare-up came as Hamas sought further steps from Israel toward easing its blockade under a previous ceasefire brokered by Egypt and the United Nations.
Israel faced pressure to seek to restore calm and put an end to the rocket fire hitting communities in the country's south.