Israeli Prime Minister Ehud Olmert ordered Israel's army to observe a ceasefire from 2:00 a.m. Monday (2300 GMT Sunday) and pull back some troops from south Lebanon, the Haaretz newspaper reported on its website.
"Olmert ordered the army to begin abiding by it as of 2:00 a.m. this morning, other than in cases of self-defense," the report said.
"They also agreed that the army will begin withdrawing some of its forces from Lebanon immediately, but will remain in various positions that offer control over surrounding areas until these positions can be handed over to the Lebanese Army and the UN Interim Force in Lebanon (UNIFIL)," it said.
Olmert's ceasefire order was six hours ahead of the UN Security Council prescribed truce between Israeli forces and Hezbollah guerrillas, which takes effect at 0500 GMT.
The paper also reported that Olmert had met his defense minister and heads of armed forces late on Sunday to discuss the ceasefire.
The Security Council resolution, adopted unanimously on Friday, called on Israeli troops to withdraw and an increase of existing UN force in Lebanon to 15,000 troops.
Israel has launched massive offensive attacks in Lebanon since Lebanese Hezbollah guerrillas kidnapped two Israeli soldiers on July 12. The 33-day fighting has killed some 1,100 Lebanese, mostly civilians, and 149 Israelis, including 109 soldiers.