Leaders of Lebanon and Israel have urged their governments to accept the proposal which was passed on Friday night, although fighting looks set to continue at least until the end of the weekend.
"Lebanon has been a victim for too long," Kofi Annan, the UN secretary general, said.
Condoleezza Rice, the US secretary of state, said that the UN text should "open a path to lasting peace between Lebanon and Israel that will end the suffering and violence of this past month".
Although the Israeli prime minister endorsed the resolution, he also authorised the Israeli army to continue to expand its ground offensive against Hezbollah before his cabinet votes on the resolution on Sunday.
The unanimous vote in New York ended weeks of negotiations to end fighting which has killed at least 1,000 people since Hezbollah captured two Israeli soldiers in a cross-border raid on July 12.
The resolution approved by the 15-nation Security Council now authorises the deployment of 15,000 UN troops to monitor a withdrawal of Israeli troops from southern Lebanon and to help the Lebanese army enforce a ceasefire.
The Lebanese government accepted the resolution and would issue a formal acceptance on Saturday, an official source said late on Friday.
Ehud Olmert told George Bush, the US president, that he backed the resolution, an Israeli government official said.
"The prime minister spoke with President Bush and thanked him for his assistance in keeping Israeli interests in mind at the Security Council," the official said.
Olmert will urge his cabinet to approve the UN resolution at a meeting on Sunday.
An Israeli official said before the vote, however, the Israeli army would not stop its offensive in Lebanon until the cabinet met on Sunday to consider the resolution.
Earlier, Olmert ordered an expansion in the ground offensive against Hezbollah.
Airstrikes have taken a massive toll on Lebanon's infrastructure
On Saturday morning long columns of Israeli troops and vehicles were reported to be crossing the Lebanese border to reinforce forces already in southern Lebanon.
The continuing offensive comes after continued Israeli airstrikes continued to target suspected Hezbollah positions, vehicles and individuals across Lebanon.
Israeli attacks had killed at least 26 people in Lebanon on Friday, seven of them when a drone fired rockets at a convoy of hundreds of cars fleeing the south.
An Israeli soldier was killed in fighting and Hezbollah fired more than 50 rockets into Israel wounding seven people.
An ambiguous resolution
Although international leaders hailed the resolution, its text contains many ambiguities that may prevent peace from taking hold.
In particular, the resolution says that UN peace-keeping force will deploy only "on a full cessation of hostilities".
With Hezbollah forces locked in combat with Israeli forces across a wide stretch of southern Lebanon, it is not clear how this will happen.
The resolution also does not say what will happen if sporadic fighting continues. It does not empower any UN force to separate the warring sides, or specify any punishments against any army that fails to entirely halt "hostilities".
Only after fighting stops, the resolution says, should Israel withdraw all its forces from southern Lebanon at the earliest opportunity. Lebanon is due to deploy its armed forces throughout southern Lebanon as Israel withdraws.
And although the resolution says only armed forces belonging to the Lebanese army or the United Nations should remain south of the Litani river, it does not say that Hezbollah should be disarmed, as Israel had previously demanded.
"A ceasefire that is incomplete is not a true ceasefire"
Tarek Mitri, Lebanon's acting foreign minister
The resolution also does not specifically demand the safe return of the two Israeli soldiers whose capture exactly a month ago sparked the conflict. Neither does it say what will happen to Hezbollah fighters captured by Israel.
It is also unclear where the 15,000 UN troops will come from. Many countries are unwilling to deploy combat troops in a region deeply hostile to foreign intervention.
Tarek Mitri, Lebanon's acting foreign minister, complained that the resolution only calls on Israeli troops to halt all "offensive" operations but does not insist on an immediate halt to fighting.
"A ceasefire that is incomplete is not a true ceasefire. A ceasefire that retains for one side the right not to cease firing is not a ceasefire," he said.