"This is a breakthrough arrived at through hard-fought diplomacy," a senior State Department official said about the resolution.
"The Russians have agreed to support a strong, binding and enforceable resolution that unites the pressure and focus of the international community on the Syrian regime to ensure the elimination of Syria's chemical weapons," the official said.
According to a draft obtained by CNN, the resolution requests the director general of the OPCW and the U.N. secretary general report noncompliance to the Security Council. In the event of noncompliance, the council would impose measures under Chapter VII of the United Nations Charter.
Russia was the one to offer a proposal that Obama and others have embraced -- to eliminate the Syrian government's chemical weapons stockpile.
Defense Minister Sergei Shoigu has said his country is willing to transport and destroy Syrian chemical weapons, although only as part of an international coalition.
Russia and the United States agreed earlier this month on the framework for such a plan. This came soon after Russian President Vladimir Putin took to The New York Times to argue against military intervention in Syria.
Striking Syria would have many negative ramifications, Putin argued in the piece, including the killing of innocent people, spreading violence around the Middle East, clouding diplomatic efforts to address Iran's nuclear crisis and resolve the Israeli-Palestinian conflict and "unleash(ing) a new wave of terrorism."