The UN Security Council has backed a no-fly zone over Libya and "all necessary measures" to protect civilians short of an occupation.
It was not immediately clear what form intervention would take and when it would begin, though France signalled that action could start soon.
The resolution appears to give legal weight to attacks against Col Muammar Gaddafi's ground forces.
Col Gaddafi's forces have recently retaken several towns seized by rebels.
Rebel forces reacted with joy to the UN resolution in their Benghazi stronghold, but a government spokesman condemned UN "aggression".
Loyalist forces are bearing down on Benghazi, home to a million people.
Following the UN vote, US President Barack Obama called the French and British leaders to discuss the next move. They said Libya had to comply immediately with the resolution.
"Given the critical situation on the ground, I expect immediate action on the resolution's provisions," said UN Secretary-General Ban Ki-moon.
"Strikes will take place rapidly," French government spokesman Francois Baroin said on Friday morning. But he added: "You will understand that there's no question of talking as early as this morning about when, how, which targets or in which form."
It is not thought that the US would be involved in the first strikes. The British and French, along with some Arab allies, are expected to play a leading role. Norway has said it will also participate.
BBC diplomatic correspondent Jonathan Marcus says signals from Paris suggest that air operations could be imminent, but this may be an attempt to keep Col Gaddafi guessing.
US officials said an attempt to ground Col Gaddafi's air force could begin on Sunday or Monday.
The UK, France and Lebanon proposed Security Council Resolution 1973, with US support.
In New York, the 15-member Security Council voted 10-0 in favour, with five abstentions.
Russia and China - which often oppose the use of force against a sovereign country as they believe it sets a dangerous precedent - abstained rather than using their power of veto as permanent members.
'Killing must stop'
French Foreign Minister Alain Juppe, introducing the resolution, said: "In Libya, for a number of weeks the people's will has been shot down... by Colonel Gaddafi who is attacking his own people.
"We cannot let these warmongers do this, we cannot abandon civilians."
He added: "We should not arrive too late."
The US ambassador to the UN, Susan Rice, said: "This resolution should send a strong message to Colonel Gaddafi and his regime that the violence must stop, the killing must stop and the people of Libya must be protected and have the opportunity to express themselves freely."
But Germany, which abstained, will not be contributing to the military effort. Foreign Minister Guido Westerwelle said his government sees "considerable dangers and risks" in military action against Col Gaddafi.
Chinese foreign ministry spokeswoman Jiang Yu said Beijing had "serious reservations" about the resolution but did not veto it "in view of the concerns and stance of the Arab countries and African Union and the special circumstances that currently apply in Libya".
In rebel-held Benghazi, locals cheered, fired guns in the air and let off fireworks to celebrate the imminent no-fly zone.
But Libya's Deputy Foreign Minister Khaled Kaaim said the vote amounted to "a call for Libyans to kill each other", AFP news agency reported.
"This resolution shows an aggressive attitude on the part of the international community, which threatens the unity of Libya and its stability," he was quoted as saying.
Shortly before the vote, Col Gaddafi told Portuguese television: "If the world is crazy, we will be crazy too."
Earlier on Thursday, addressing the people of Benghazi, Col Gaddafi said his troops were coming "tonight" and there would be "no mercy".
Shortly before the UN vote on Thursday, anti-aircraft fire and explosions were heard in Benghazi, where forces loyal to Col Gaddafi reportedly launched their first air attacks, targeting the airport at Benina.
The Libyan military earlier warned that civilian and military activities in the Mediterranean would become "the target of a Libyan counter-attack" following any foreign operation.
In other developments:
- Col Gaddafi's forces were reported to be bombarding the city of Misrata. Libyan state TV had claimed the city was almost entirely under government control, but rebels and residents denied this
- Pro-Gaddafi forces attacked the rebel-held town of Ajdabiya, a key objective before launching a ground assault on Benghazi, but rebels deployed tanks, artillery and a helicopter to repel the assault
- Official Libyan news agency Jana reported that government forces would cease military operations from midnight on Sunday to give rebels the opportunity to hand over their weapons and "benefit from the decision on general amnesty"
Following the toppling of the long-time leaders of neighbouring Tunisia and Egypt earlier this year, Libyan protesters started to demand that Col Gaddafi step down after more than 40 years of autocratic rule.