Money will also be given to soldiers who defect from the government's army, the SNC added, after a "Friends of the Syrian people" summit in Turkey.
Conference delegates said wealthy Gulf Arab states would supply millions of dollars a month for the SNC fund.
The meeting recognised the SNC as the "legitimate representative" of Syrians.
Damascus dubbed the gathering of some 70 Western and Arab foreign ministers in Istanbul as the "enemies of Syria", and key players remained absent, including Russia, China and Iran.
At a news conference, Turkish Foreign Minister Ahmet Davutoglu warned Syria that Kofi Annan's six-point peace plan - which Damascus has agreed to in principle - was "not open-ended".
His comments were echoed by US Secretary of State Hillary Clinton who said there was "no more time for excuses and delays" by the Assad government. "This is a moment of truth," she said.
"The SNC will take charge of the payment of fixed salaries of all officers, soldiers, and others who are members of the Free Syrian Army," SNC President Burhan Ghalioun told the conference.
An SNC leader told the BBC that she hoped more substantial funding would help bind the disparate units of the Free Syrian Army into a more coherent fighting force, and encourage other soldiers to defect from the government side.
Some countries at the conference - notably Saudi Arabia - have been openly calling for insurgents in Syria to be given weapons. But others - including the US and Turkey - oppose the move, fearing it could fuel an all-out civil war.
The decision to increase non-lethal aid to the rebels by paying salaries to the fighters is a compromise, the BBC's Jonathan Head in Istanbul says.
Not all opposition groups will be happy at the summit's decision to channel the funds through the SNC - as well as recognising it as the legitimate representative of the Syrian people, he adds.
There are many activists who believe the SNC's leadership has been too ineffective, and should be replaced, he points out.
The united front displayed by the gathering was undermined by the pointed absence of Russia and China, which have repeatedly balked at any international resolutions that would require President Assad to stand down.
Iraq attended, having earlier suggested it might not. However, Prime Minister Nouri al-Maliki made it clear beforehand that he opposed arming the opposition and believed the Syrian government would survive.
The Syrian government says it is close to ending the uprising.
Syrian foreign ministry spokesman Jihad al-Makdissi told Syrian TV "the battle to topple the state is over".
Violence continued on Sunday, with more than 10 people reported killed, a day after more than 60 people died across the country.
In the latest violence, activists reported attacks by security forces in areas near the Iraqi border to the east, and the Jordanian frontier to the south.
The UN believes at least 9,000 people have died in the year-long revolt against Mr Assad's rule.