The imminent transfer of power follows 13 years of civil war and the end to more than 50 years of brutal rule by the Assad family, leaving Syrians at home and millions of refugees abroad hopeful yet deeply uncertain about their country's future.
Damascus stirred to life on Monday, with traffic returning to streets and people venturing out after a nighttime curfew, but most shops remained shut.
Fighters from the remote countryside milled about in the capital, clustering in the central Umayyad Square.
Two women, whose relatives were imprisoned, react to the news of the fall of the Assad regime. (AP PHOTO)
Assad's Prime Minister, Mohammed Jalali, told Al Arabiya TV he had agreed to hand power to the Salvation Government, an administration based in a small pocket of rebel-held territory in northwest Syria.
He said the handover could take days to carry out.
The main rebel commander Ahmed al-Sharaa, better known as Abu Mohammed al-Golani, had met overnight with Jalali and Vice President Faisal Mekdad to discuss a transitional government, a source familiar with the discussions told Reuters.
Al Jazeera television reported the transitional authority would be headed by Mohamed al-Bashir, who ran the Salvation Government before the 12-day lightning offensive that swept into Damascus.
A source close to the rebels in Idlib confirmed Bashir had been nominated, though there had been no official announcement.
The advance of a militia alliance spearheaded by Hayat Tahrir al-Sham (HTS), a former al Qaeda affiliate, was a generational turning point for the Middle East.
It ends a war that killed hundreds of thousands of people, caused one of the biggest refugee crises of modern times and left cities bombed to rubble, countryside depopulated and the economy hollowed out by global sanctions. Refugees could finally go home from camps across Turkey, Lebanon and Jordan.
Assad's fall wipes out one of the main bastions from which Iran and Russia wielded regional power. Turkey, long aligned with Assad's foes, emerges strengthened.
The Arab world faces the task of reintegrating one of the Middle East's pivotal states, while containing the militant Sunni Islam that has in the past metastasised into the sectarian violence of Islamic State.
HTS is still designated as a terrorist group by the United Nations, but has spent years trying to soften its image to reassure foreign states and minority groups within Syria.
The rebels announced on their Telegram channel they were granting amnesty to all conscript soldiers drafted under Assad.
Assad's police state was known for generations as one of the harshest in the Middle East, holding hundreds of thousands of political prisoners. On Sunday, elated inmates poured out of jails.
One of the final areas to fall was the Mediterranean coast, heartland of Assad's Alawite sect and site of Russia's naval base.
Crowds gather outside the infamous Saydnaya military prison, just north of Damascus, Syria. (AP PHOTO)
The Kremlin said it was too early to know the future of Russia's military bases in Syria, but it would discuss the issue with the new authorities.
Israel said Assad's fall was a direct consequence of Israel's punishing assault on Iran's Lebanese allies Hezbollah, who had propped up Assad for years.
Since rebels entered Damascus, Israel has struck sites in Syria. Israeli officials said those airstrikes would carry on for days to keep Assad's former arsenal out of hostile hands.
The United States, which has 900 soldiers in Syria alongside Kurdish-led forces in the east, said its forces hit around 75 targets in airstrikes on Islamic State on Sunday.
