US Secretary of State John 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," Kerry told reporters at a joint press conference with Russian Foreign Minister Sergei Lavrov.
Echoing a warning from President Barack Obama that military action by the US and its allies remained an option if diplomacy fails, Kerry warned that there must be "no games, no room for avoidance of anything less than full compliance by the Assad regime."
Kerry said the steps agreed on Saturday 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 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 signalled that Moscow would back some form of sanction, saying the Security Council would act under Chapter Seven if Syria fails to meet its demands.
Kerry said that Syria's bloody civil war, which has resulted in more than 110,000 deaths in two and a half years, could only be ended through negotiations.
That was another nod to Russia's opposition to any form of military intervention and could be interpreted as the United States backing away from providing support for the rebels to help them force Assad from power.
"There is no military solution to the conflict in Syria, it has to be political," Kerry said. "And we together remain committed to getting there."
Lavrov hailed Saturday's accord as an "excellent" agreement "whose significance is hard to overestimate."
The accord was greeted with dismay by the Syrian opposition coalition, who have spent two years appealing to the west to give them the weapons needed to tilt the balance of the civil war in their favour.
"We cannot accept any part of this initiative," General Selim Idriss, the head of the Free Syrian Army, 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."
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.
Washington and Moscow hope to revive plans for peace talks in Geneva that would bring together Assad's regime and the opposition to agree a political transition to end the war that erupted in March 2011.
Kerry and Lavrov will meet again in a few weeks on the sidelines of the UN General Assembly in New York, with the hope of setting a date for the stalled peace conference.
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, which Washington blames on the regime and says killed about 1,400 people.
France on Saturday welcomed the Geneva deal as a breakthrough. "The plan is a significant step forward," Foreign Minister Laurent Fabius said.
The United States has estimated that Syria possesses around 1,000 metric tonnes of various chemical agents, including mustard and sarin gas, sulfur and VX.
The Russian estimates had been initially much lower, according to US officials, but Kerry said Saturday that the two countries had reconciled their different assessments.
US officials said there were around 45 sites that inspectors would have to check out and Kerry said it would be feasible to do that, despite the fighting.
"One of the reasons we believe this is achievable is because the Assad regime has taken extraordinary means to keep control of these weapons," he added, noting that the chemical weapons were mainly in regions under Damascus' control.
"So that's the silver lining. We should not have a problem achieving access to these sites and that will soon be put to the test," he added.
Despite the upbeat tone of Saturday's press conference, Kerry acknowledged that "a hard road" lies ahead amid widespread scepticism about Assad's good faith.
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.
Kerry flies to Israel on Sunday to brief Prime Minister Benjamin Netanyahu.
He will then travel to Paris for a Monday meeting with Fabius and British Foreign Secretary William Hague as well as the Saudi Foreign Minister Saud al-Faisal.