The leadership of the 120,000 Armenians who call Karabakh home say they did not want to live as part of Azerbaijan and that they would leave for Armenia because they feared persecution and ethnic cleansing.
In the Karabakh capital, known as Stepanakert by Armenia and Khankendi by Azerbaijan, crowds of people were loading belongings into buses and trucks on Monday as they left for Armenia.
Refugees who reached Armenia said they believed the history of their breakaway state was finished.
"No one is going back - that's it," Anna Agopyan, who reached Goris, a border town in Armenia, said. "The topic of Karabakh is over now for good I think."
Srbuhi, a mother of three who reached Armenia, shed tears as she held her young daughter.
"I left everything there," she said.
The Armenian government, making preparations for thousands of refugees, said that as of 8am local time on Monday, at least 4850 people from Nagorno-Karabakh had crossed into Armenia.
The ethnic Armenian leadership said it would remain in place until all those who wanted to leave what they call Artsakh were able to go. Meanwhile, they urged residents to hold back from crowding the roads out, to allow the evacuation of the injured.
"We inform you that all citizens who wish to move from Artsakh to Armenia will have that opportunity," the leadership said. It said free fuel would be provided later on Monday for all those who wanted to leave the territory.
The Armenians of Karabakh, a territory internationally recognised as part of Azerbaijan, were forced into a ceasefire last week after a 24-hour military operation by the much-larger Azerbaijani military.
Azerbaijan's President Ilham Aliyev was due to host his ally Turkish President Tayyip Erdogan on Monday in the autonomous Nakhchivan exclave - a strip of Azerbaijani territory separated from the rest of the country by Armenia.
They will attend a ceremony for a gas pipeline that will bring gas to Nakhchivan and inaugurate a newly modernised military installation in the exclave, Turkey said.
The Azerbaijani victory alters the delicate balance of power in the South Caucasus region, a patchwork of ethnicities crisscrossed with oil and gas pipelines where Russia, the US, Turkey and Iran are jostling for influence.
Since the breakup of the Soviet Union, Armenia had relied on a security partnership with Russia, while Azerbaijan grew close to Turkey, with which it shares linguistic and cultural ties.
The US has said it was deeply concerned by Azerbaijan's military operation, which Baku launched on September 19 after what it said were terrorist attacks on its civilians by Karabakh fighters.
The Armenians of Karabakh said Russia, the West and Armenia itself had abandoned them, and some spoke through tears of the end of an era for the Karabakh Armenians.
Petya Grigoryan, a 69-year-old driver, said his village in what the Armenians know as the Martakert district of Karabakh had been pummelled by Azerbaijan armed forces.Â
There were two truckloads full of dead civilians in the village, he said.
"There was nowhere to bury them," Grigoryan said.
Of the 500 villagers, he said 40 had got out.
Reuters was unable to independently verify his account but it chimed with the outline given by other ethnic Armenians fleeing Karabakh, which Azerbaijan says will be turned into a "paradise" and fully integrated.
Azerbaijan's victory reverses a humiliating defeat the country suffered as the Soviet Union broke up, which left around a seventh of its population homeless and Armenians in control of swathes of territory around Karabakh.
