Syria's army command notified officers on Sunday that Assad's regime had ended, a Syrian officer who was informed of the move told Reuters news agency.
But the Syrian army later said it was continuing operations against "terrorist groups" in the towns of Hama and Homs and Deraa countryside.
Assad, who had crushed all forms of dissent, flew out of Damascus for an unknown destination earlier on Sunday, two senior army officers said, as rebels said they had entered the capital with no sign of army deployments.
We met someone on the Lebanese side of the border who was crying because he was so frustrated. He was afraid that he would be targeted by the rebels, so he was trying to get his family out, and he hasn't been able to do that.
I think many people are going to be keeping a low profile for the next few days.
You also have this rejoicing, with many people feeling that there has been a very authoritarian regime for decades.
It was significant that one of the first things the rebels did was go to the prison to release the inmates, among them probably many political dissidents who had been detained and tortured. That was one of the many prisons infamous for that.
One of the crucial things is going to be how coordinated this all is.
Thousands in cars and on foot congregated at a main square in Damascus waving and chanting "Freedom" after a half-century of Assad family rule, witnesses said.
The dramatic collapse marks a seismic moment for the Middle East, ending the family's iron-fisted rule over Syria and dealing a massive blow to Russia and Iran, which have lost a key ally at the heart of the region.
"We celebrate with the Syrian people the news of freeing our prisoners and releasing their chains and announcing the end of the era of injustice in Sednaya prison," the rebels said, referring to a large military prison on the outskirts of Damascus where the Syrian government detained thousands.
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The aircraft initially flew towards Syria's coastal region, a stronghold of Assad's Alawite sect, but then made an abrupt U-turn and flew in the opposite direction for a few minutes before disappearing off the map.Reuters could not immediately ascertain who was on board.
The head of Syria's main opposition group abroad, Hadi al-Bahra Syrian, declared Damascus was now "without Bashar al-Assad". Syrian prime minister 'ready for handover procedures'
As Syrians expressed joy, Prime Minister Mohammad Ghazi al-Jalali said he was ready to support the continuity of governance and prepared to cooperate with any leadership chosen by the Syrian people.
In a speech broadcast on his Facebook account, Jalali said "this country can be a normal country that builds good relations with its neighbours and the world".
"But this issue is up to any leadership chosen by the Syrian people. We are ready to cooperate with it (that leadership) and offer all possible facilities," he added.
US President Joe Biden and his team were monitoring the "extraordinary events in Syria" and were in touch with regional partners, the White House said.
The frontlines of Syria's complex civil war were dormant for years. Then Islamists once affiliated with al-Qaeda suddenly burst into action, posing the biggest challenge to Assad, who had survived years of gruelling war and international isolation with the help of Russia, Iran and Lebanon's Hezbollah.
But Assad's allies were focused on and weakened by other crises, leaving Assad at the mercy of his opponents with an army that was not prepared to defend him.
Syrian rebel leader Ahmed al-Sharaa said on Sunday that it was prohibited to go near public institutions that he said will remain under the supervision of the "former prime minister" until they were officially handed over.
Israel, which has severely weakened the Iran-backed groups Hezbollah in Lebanon and Hamas in Gaza, will likely celebrate the fall of Assad, another of Iran's key regional allies. But the prospects of an Islamist group ruling Syria will likely raise concerns.
Just hours before reaching Damascus, rebels announced they had gained full control of the key city of Homs after only a day of fighting, leaving Assad's 24-year rule dangling by a thread.
Thousands of Homs residents poured onto the streets after the army withdrew from the central city, dancing and chanting "Assad is gone, Homs is free" and "Long live Syria and down with Bashar al-Assad".
The fall of Homs gave the insurgents control over Syria's strategic heartland and a key highway crossroads, severing Damascus from the coastal region that is the stronghold of Assad's Alawite sect and where his Russian allies have a naval base and air base.
Homs' capture is also a powerful symbol of the rebel movement's dramatic comeback in the 13-year-old conflict. Swathes of Homs were destroyed by gruelling siege warfare between the rebels and the army years ago. The fighting ground down the insurgents, who were forced out.
Hayat Tahrir al-Sham commander Abu Mohammed al-Golani, the main rebel leader, called the capture of Homs a historic moment and urged fighters not to harm "those who drop their arms".
Rebels freed thousands of detainees from the city prison. Security forces left in haste after burning their documents.
Syrian rebel commander Hassan Abdul Ghani said in a statement early Sunday that operations were ongoing to "completely liberate" the countryside around Damascus and rebel forces were looking toward the capital.
In one suburb of Hama, a statue of Assad's father, the late President Hafez al-Assad, was toppled and torn apart. Source: Getty / Muhammad Haj Kadour
How did Assad's rule come under threat?
The pace of events has stunned Arab capitals and raised fears of a new wave of regional instability.
Qatar, Saudi Arabia, Jordan, Egypt, Iraq, Iran, Turkey and Russia issued a joint statement saying the crisis was a dangerous development and calling for a political solution.
Syria's civil war, which erupted in 2011 as an uprising against Assad's rule, dragged in big outside powers, created space for jihadist militants to plot attacks around the world and sent millions of refugees into neighbouring states.
Hayat Tahrir al-Sham, the strongest rebel group, is the former al-Qaeda affiliate in Syria regarded by the US and others as a terrorist organisation, and many Syrians remain fearful it will impose draconian Islamist rule.
Golani has tried to reassure minorities that he will not interfere with them and the international community that he opposes Islamist attacks abroad. In Aleppo, which the rebels captured a week ago, there have not been reports of reprisals.
When asked on Saturday whether he believed Golani, Russian Foreign Minister Sergei Assad's long rule relied on allies to subdue the rebels. Russian warplanes conducted bombing while Iran sent allied forces including Hezbollah and Iraqi militia to reinforce the Syrian military and storm insurgent strongholds.
But Russia has been focused on the war in Ukraine since 2022 and Hezbollah has suffered big losses in its own gruelling war with Israel, significantly limiting its ability or that of Iran to bolster Assad.
US President-elect Donald Trump has said the US should not be involved in the conflict and should "let it play out".
The United Arab Emirates has said it remains “very worried” by threats to the territorial integrity of Syria and the risk that the country may succumb to extremism and terrorism.
“Syria is still not out of the woods,” said Anwar Gargash, diplomatic adviser to the President of the UAE. “We hope the Syrians will work together, that we don't just see another episode of impending chaos.”
Gargash, one of the most experienced and respected diplomats in the Gulf, was addressing the Manama Dialogue security conference in Bahrain, organised by the London-based think tank, the International Institute for Strategic Studies.
He said he did not know where Bashar al-Assad was but did not deny suggestions that Syria’s former president might live in exile in Abu Dhabi. He said the question was not important, a “footnote in history” like where Germany’s Kaiser Wilhelm lived after WWI.
“When people are asked, you know, where is Bashar al-Assad, I say when you look at this, at the end of the day, this is a footnote in history,” he said. “I am reminded a little bit by Kaiser Wilhelm the second in 1918 who went to a long exile that he spent for many years, many people think in Holland. I don’t think when you look at that period, I don’t think that his is really critical.”