The measure to be voted on next week sets a time limit of 60 days on any operation. The draft document also bans the use of any ground forces in Syria.
Secretary of State John Kerry said the US had to act after the "undeniable" chemical weapons attack in Syria.
The Republican Speaker of the House of Representatives, John Boehner, endorsed Obama's call for military action.
According to a copy of the draft resolution, the senators wish to restrict the operation to a "limited and tailored use of the United States Armed Forces against Syria."
The resolution states that "the president may extend" a 60-day operation "for a single period of 30 days" if he obtains further specific Congressional approval.
"The authority granted... does not authorize the use of the United States Armed Forces on the ground in Syria for the purpose of combat operations," the statement added.
The draft was released after Kerry appeared before the Senate Foreign Relations Committee.
The secretary of state claimed there was evidence beyond any reasonable doubt that the Syrian troops prepared for a chemical weapons attack near Damascus on 21 August.
Kerry told the senators the president was not asking America to go to war. "He is asking only for the power to make clear, to make certain, that the United States means what we say."
Standing aside, he claimed, would allow other countries to pursue weapons of mass destruction.
"This is not the time for armchair isolationism," Kerry added . "This is not the time to be spectators to slaughter.''
US Defense Secretary Chuck Hagel and the top US military officer, Gen Martin Dempsey, also appeared before the Senate panel.
The call for military action against Syria intensified after foreign-backed opposition forces accused the government of President Bashar al-Assad of launching a chemical attack on militant strongholds in the suburbs of Damascus on August 21.
Damascus has vehemently denied the accusations, saying the chemical attack was carried out by the militants themselves as a false-flag operation.
Syria says it will retaliate any attack on the country with full force.
BA/BA