The draft resolution's demands that Syria abandon its chemical stockpile and allow unfettered access to chemical weapons experts are legally binding.
But if Syria fails to comply, the council will need to adopt a second resolution to impose measures that allow for military and non-military actions to promote peace and security.
Nonetheless, after two-and-a-half years of inaction and paralysis, the agreement represents a breakthrough for the security council and is a rare demonstration of unity between Russia, which supports Syrian president Bashar al-Assad's government, and the US, which backs the opposition.
Russia and the US jointly introduced the text to the 10 non-permanent council members, supported by the other permanent members Britain, France and China.
A vote on the resolution depends on how the full council responds to the draft and on how soon an international group that oversees the global treaty on chemical weapons can adopt a plan for securing and destroying Syria's stockpile.
The spark for the recent flurry of diplomatic activity was the August 21 poison gas attack that killed hundreds of civilians in a Damascus suburb and President Barack Obama's threat of US strikes in retaliation.
After US secretary of state John Kerry said Mr Assad could avert US military action by turning over "every single bit of his chemical weapons" to international control within a week, Russia agreed.
Mr Kerry and Russian foreign minister Sergey Lavrov signed an agreement on September 13 to put Syria's chemical weapons under international control for later destruction, and Mr Assad's government accepted.
"Just two weeks ago, tonight's outcome seemed utterly unimaginable," US ambassador Samantha Power said after the security council meeting. "Two weeks ago the Syrian regime had not even acknowledged the existence of its chemical weapons stockpiles.
"If implemented fully, this resolution will eliminate one of the largest previously undeclared chemical weapons programmes in the world."
Britain's UN ambassador Sir Mark Lyall Grant and a senior US State Department official described the draft resolution as "binding and enforceable".
The draft resolution makes clear there is no trigger for enforcement measures if Syria fails to comply. The Russian, US and British ambassadors confirmed this would require a second resolution. However, Sir Mark said the strong language in the text requires members to act.
Negotiations on the draft resolution were said to have been tough. Russia and China have vetoed three previous Western-backed resolutions aimed at pressuring Mr Assad to end the violence, but the chemical weapons attack proved to be a turning point.
Meanwhile, it emerged yesterday that inspections of Syria's chemical arsenal will begin by Tuesday under a disarmament plan to be discussed by the global chemical weapons watchdog.
The draft decision of the Organisation for the Prohibition of Chemical Weapons also authorises the body to inspect "any other site identified by a State Party as having been involved in the Syrian chemical weapons programme, unless deemed unwarranted by the Director-General".
That goes beyond usual practice, as the organisation has only previously inspected sites declared by member states.
The draft decision also sets out a clear and ambitious timeline for the verification and destruction of Syria's weapons.