The landmark agreement, announced in Geneva on Saturday, left the door open to unspecified sanctions if Damascus fails to comply, and was swiftly hailed by the West.
However it was equally swiftly rejected by Syrian rebels who warned it would not halt the bloodshed in the conflict that has killed more than 110,000 people and displaced millions in two and a half years.
Under the accord struck in three days of talks in Geneva between US Secretary of State John Kerry and his Russian counterpart Sergei Lavrov, Syrian President Bashar al-Assad now has a week to hand over details of his regime's stockpile.
Kerry said Assad's regime must also provide "immediate and unfettered" access to inspectors from the Organisation for the Prohibition of Chemical Weapons (OPCW).
"The inspectors must be on the ground no later than November... and the goal is to establish the removal by halfway through next year," said Kerry, flanked by Lavrov.
The pressure is now on Assad to deliver, with US President Barack Obama warning that "the United States remains prepared to act" if Damascus fails to comply.
But influential US Senators John McCain and Lindsey Graham said the agreement was a debacle.
In a joint statement, the two Republican lawmakers voiced fear that Washington's friends and foes alike will view the agreement as an "act of provocative weakness on America's part."
Kerry said the agreed steps would be encapsulated in a UN Security Council resolution drawn up under Chapter Seven of the organisation's charter, which provides for enforcement through sanctions, including the possible use of military force.
But with Russia strongly opposed to the use of military threats against its long-term ally Syria, and wielding a veto on the Security Council, Kerry acknowledged it was "impossible to have a pre-agreement" on what would happen in the event of non-compliance.
Lavrov hailed the accord as an "excellent" agreement "whose significance is hard to overestimate."
Kerry flies to Israel on Sunday to brief Prime Minister Benjamin Netanyahu about the deal and discuss the Israeli-Palestinian peace process, kicking off a flurry of diplomatic activity.
He will travel to Paris for a Monday meeting with French counterpart Laurent Fabius and British Foreign Secretary William Hague, as well as the Saudi Foreign Minister Saud al-Faisal.
Meanwhile, French Foreign Minister Laurent Fabius will visit veto-wielding China on Sunday to discuss Syria.
On his way back, Fabius will hold talks on Tuesday with Lavrov amid an intense few days of negotiations between the permanent members of the Security Council.
France has been one of Washington's closest allies in urging military action in response to an August 21 chemical attack on the outskirts of Damascus blamed by Washington and others on the Syrian government.
In contrast, both China and Russia have consistently blocked resolutions at the UN to sanction the Syrian regime.
The British parliament has voted against participating in any military action against Assad.
Syrian rebels fighting the Assad regime greeted the US-Russia plan with dismay, fearing it has scuppered any chance of Western military intervention on their side.
"We cannot accept any part of this initiative," Free Syrian Army chief General Selim Idriss told reporters in Istanbul.
"Are we Syrians supposed to wait until mid-2014, to continue being killed every day and to accept (the deal) just because the chemical arms will be destroyed in 2014?"
Iran, one of Assad's main allies, said the United States no longer has a pretext to attack Syria.
Kerry said that Syria's bloody civil war could only be ended through negotiations, and promised to meet with Lavrov again soon, this time in New York, to try to breathe life into planned peace talks between the regime and the opposition.
Washington and Moscow hope to secure a political transition to end the conflict that began in March 2011 with peaceful protests against the Assad regime and quickly turned violent following a brutal government crackdown of the demonstrations.
Fighting on the ground in Syria continued unabated, with rebel and regime forces engaged in a fierce battle for control of the ancient Christian town of Maalula, near Damascus.
Russia's surprise announcement that Syria could hand over its chemical arsenal prompted Obama to put on hold military strikes the United States and France had threatened to unleash in response to an August chemical attack near Damascus.
The United States and Russia now agree that Syria possesses around 1,000 metric tonnes of various chemical agents, including mustard and sarin gas, sulphur and VX.
US officials also said there were around 45 sites that inspectors would have to check and Kerry said it would be feasible to do that, despite the fighting.
EU foreign policy chief Catherine Ashton offered the bloc's help with "securing sites and in dismantling and destroying certain chemical agents."
NATO in turn welcomed the agreement, saying that "full and unreserved Syrian compliance is now key."
UN chief Ban Ki-moon has accused Assad of multiple crimes against humanity and said that a UN inspectors' report due to be published on Monday would provide "overwhelming" confirmation that chemical weapons were used on August 21.