The vote on Saturday marked the first time UN diplomats on the council all agreed on a resolution since the conflict began more than a year ago.
It calls on both sides to immediately "cease all armed violence in all its forms". It also calls on the Syrian government to implement the six-point peace plan put forward by international envoy Kofi Annan, including the pull-back of troops and heavy weapons from cities and town.
The resolution calls for the deployment of an advance team of up to 30 unarmed military observers to initiate contacts with both sides and begin to report on whether there has been "a full cessation of armed violence in all its forms by all parties".
The council said it intends to immediately establish a larger UN supervision mission after consultations between Ban Ki-moon, the UN secretary-general, and the Syrian government.
Deployment of a larger force will be "subject to a sustained cessation of armed violence in all its forms by all parties".
Annan's spokesman, Ahmad Fawzi, has said that Annan, who is an envoy on behalf of the UN and the Arab League, envisions a mission with about 250 observers.
Swift action
The first five or six UN ceasefire monitors will be in Syria on Sunday, a UN peacekeeping spokesman said.
"Immediately (after) the Security Council passed the resolution today, we had five or six military observers getting on a plane. They will arrive in Syria probably tomorrow," Kieran Dwyer told AFP news agency.
Bashar Ja'afari, the Syrian UN ambassador responded to the resolution by first citing the capture and confession of two Syrian youth hired to commit crimes as examples of armed military groups in the country.
He then affirmed support for Annan's six-point plan.
"While we feel that this resolution was not balanced, Syria affirms that it is in its interest to guarantee the return of security and stability to the country. We hope that the countries who abide by this resolution would implement it practically and would not send lethal or non-lethal aid to the terrorists and the armed groups," said Ja'afari.
Syria's main opposition coalition welcomed the resolution.
"We express our welcome of the decision," the Syrian National Council said in a statement signed by its leader Burhan Ghalioun, reported AFP.
"We are ready to act to make the Annan plan a success," it said.
Observers prepared
Russia and China vetoed two previous resolutions that would have condemned President Bashar al-Assad's government for its bloody crackdown on protesters and raised the threat of possible further action.
They argued that the resolutions were not balanced and did not address the attacks by rebel fighters.
In the debate on the resolution adopted Saturday, Russia submitted a rival text to the US and Western-backed draft, and raised questions on Friday evening about the final draft.
But Ambassador Vitaly Churkin told reporters before Saturday's vote that Moscow "was satisfied" and would vote "yes".
The ceasefire, which formally took effect Thursday, is at the centre of Annan's peace plan, which is aimed at ending more than a year of bloodshed that has killed over 9,000 people, according to the UN.
It also aims to launch inclusive Syrian-led talks on the country's political future.
Annan called for speedy deployment of UN monitors and his spokesman Ahmad Fawzi told a news conference in Geneva on Friday that an advance team of "around 10 or 12" observers, that could quickly be increased to 30, was "standing by to board planes and to get themselves on the ground as soon as possible" once the Security Council approved their deployment.