But a number, including permanent members, expressed frustration at how long it has taken the council to act.
More than 100,000 people have died in Syria's civil war but it took the use of chemical weapons in a Damascus suburb to finally prompt the Security Council to intervene.
Its resolution demands the eradication of Syria's chemical weapons, after Russia and the United States struck a deal over how to respond to the conflict.
British Foreign Secretary William Hague said the failure of the council to act earlier had led to a climate of brutality in Syria.
And France's representative said the Security Council was finally living up to its name.
The vote by the full 15-member body came after the five permanent members agreed on a draft.
The resolution demands the eradication of Syria's chemical weapons but does not threaten automatic punitive action against President Bashar al-Assad's government if it does not comply.
It was based on a deal between made between Russia and the United States.
United Nations secretary general Ban Ki Moon said the historic resolution was the first hopeful news on Syria for a long time.
"For many months I have said that the confirmed use of chemical weapons in Syria would require a firm united response. The international community has delivered," he said.
Chemical weapons watchdog the Organisation for the Prohibition of Chemical Weapons has also voted to accept a plan to find and destroy all Syria's chemical weapons by the middle of next year.
Inspections in Syria are due to begin on Tuesday.
The United Nations also expects to convene a second peace conference in Geneva in the middle of November, as diplomatic efforts to resolve the conflict gather momentum.
