Representatives from 130 countries declared the coalition the sole representative of the Syrian people at a Friends of Syria meeting in Marrakesh.
On Thursday the US accused Bashar al-Assad’s regime of using Scud missiles against rebels.
France was the first country to recognise the opposition alliance, followed by the European Union and, on Tuesday, US President Barack Obama.
“This is an extraordinary development, because it means that all the different opposition factions have decided to join forces,” Fabius declared after the meeting. “And it has an impact on the military, because the opposition forces have decided to unite under a single military council.”
Amid fears that the opposition is dominated by Sunni Muslims and that Al Qaeda-linked groups are gaining strength in the fight against Assad, Fabius said that he had insisted the coalition respect all Syrian communities and all minorities.
Under pressure to unite, the Syrian opposition agreed last month to establish the coalition and group the various rebel forces under a supreme military council.