Austrian police said on Saturday that about 4,000 refugees had arrived from Hungary by bus at the border since the early morning hours, with many more to come.
"We estimate that around 4,000 have arrived - and I don't think that is the end of it," said Helmut Marban, spokesman for the police in the province of Burgenland, adding some already had continued their journey onward.
"The numbers could well double, if not more," he told Reuters. Separately, German police told the newswire that they expected up to 10,000 refugees to arrive in the country on Saturday from Hungary via Austria.
A special half-hourly train service was running to take people from the border to Vienna, on top of 20 buses shuttling back and forth between the Austrian capital and the border with Hungary.
After days of confrontation and chaos, Hungary's right-wing government deployed the buses to move on migrants from its capital, Budapest, and pick up over 1,000 - many of them refugees from the Syrian war - who had set off by foot on Friday down the main highway to Vienna.
Austria said it had agreed with Germany that they would allow the migrants access, waiving the rules of an asylum system brought to breaking point by Europe's worst refugee crisis since the Yugoslav wars of the 1990s.
Wrapped in blankets and sleeping bags against the rain, long lines of visibly exhausted migrants, many carrying small children, climbed off buses on the Hungarian side of the border and walked into Austria, receiving fruit and water from aid workers. Some waiting Austrians held signs that read, "Refugees welcome".
"We're happy. We'll go to Germany," said a Syrian man who gave his name as Mohammed. Another, who declined to be named, said: "Hungary should be fired from the European Union. Such bad treatment."
Hungary cited traffic safety for its decision to move the migrants on. But it appeared to mark an admission that the government had lost control in the face of overwhelming numbers determined to reach the richer nations of northern and western Europe at the end of an often perilous journey from war and poverty in the Middle East, Africa and Asia.
"Because of today's emergency situation on the Hungarian border, Austria and Germany agree in this case to a continuation of the refugees' journey into their countries," Austrian Chancellor Werner Faymann said on his Facebook page.
On Friday, hundreds broke out of an overcrowded camp on Hungary's border with Serbia; others escaped from a stranded train, sprinting away from riot police down railway tracks, while still more took to the highway by foot led by a one-legged Syrian refugee and chanting "Germany, Germany!"
The scenes were emblematic of a crisis that has left Europe groping for answers, and for unity.
By nightfall, the Keleti railway terminus in Budapest, for days a campsite of migrants barred from taking trains west to Austria and Germany, was almost empty, as smiling families boarded a huge queue of buses that then snaked out of the capital.
The migrants left shoes, clothes and mattresses scattered behind them. Helicopters circled overhead.