The resolution, drawn up by France and the US, calls on Lebanon and the UN Interim Force in Lebanon to "deploy their forces together", while calling on Israel "as that deployment begins, to withdraw all of its forces from southern Lebanon in parallel."
It says Hezbollah must end its attacks on Israel and for Israel to end "offensive military operations".
The vote came in the wake of a continuing Israeli military offensive in southern Lebanon.
Hours before the vote, Israel's Prime Minister Ehud Olmert ordered his army to prepare to widen its offensive in southern Lebanon.
Officials say Mr Olmert will ask the Israeli cabinet to endorse the the resolution at a meeting on Sunday until which time the Israeli offensive will continue.
The latest strikes saw Israeli warplanes hit a convoy carrying Lebanese security forces and civilians which had been escorted out of Marjayun in south Lebanon by UN forces who were no longer with them, killing at least five and wounding 16, police said.
At the United Nations however US Secretary of State Condoleezza Rice told the council the resolution could lay the basis for a lasting peace between Israel and Lebanon.
But UN Secretary General Kofi Annan said the time it had taken the major powers to call for a cessation of hostilities had "badly shaken" the world's faith in the council.
The first version of the text submitted by Paris and Washington a week ago had not mentioned a withdrawal and Lebanon had objected, demanding an immediate Israeli pullout after fighting ends.
The resolution authorizes "an increase in the force strength of UNIFIL to a maximum of 15,000 troops".
The UN, which currently has about 1,190 troops in southern Lebanon, would monitor the cessation of hostilities and any permanent ceasefire that is negotiated.
The force would support Lebanese armed forces as they deploy across the region now dominated by Hezbollah and which has come under intense attack in the Israeli offensive since July 12.
UN troops would also help humanitarian work in Lebanon following the devastating conflict which has seen more than 1,100 Lebanese and Israelis killed.
Lebanese leaders are reported to have examined the text, and an adviser to Prime Minister Fouad Siniora gave the resolution a cautious welcome.