For days, Hungary had blocked them from travelling by train to northern and Western Europe.
On September 5, about 4,000 people crossed the Austrian border. They were received by the Red Cross and are now moving on towards Vienna and Germany.
Austria says the migrants, many of whom had initially fled Syria, can claim asylum there or carry on to Germany.
The move comes as EU countries are struggling to agree on how to deal with an unprecedented surge of asylum seekers.
The Hungarian government eased restrictions on transit after many frustrated migrants overwhelmed police cordons and set off towards the border on foot on September 4.
Buses began picking up migrants from Keleti train station in central Budapest, where thousands had been camped.
Vehicles were also sent to take those who had decided to walk along a motorway to Austria.
On September 5, Hungarian government spokesman Zoltan Kovacs said there would be no more buses or trains to take the migrants on to Austria.
He said the transport had been arranged as a one-off, because of fears for the migrants’ safety.
As the migrants crossed the border on foot, some Austrians displayed welcome signs.
Austrian Red Cross workers at a makeshift centre greeted them with blankets and tea.
The migrants are now being taken by train and bus from the Austrian border town of Nickelsdorf to the capital Vienna.
Many hope to travel on to Germany, which says it expects 6,000 people to arrive over the weekend.
The German government has said Syrians can apply for asylum.
Germany has said it expects to take in 800,000 people this year.
Austria’s Chancellor Werner Faymann said that after talks with his German counterpart Angela Merkel, the two countries would allow in the migrants due to the “emergency situation” in Hungary.
However, he said he expected Hungary to respect any EU quotas for asylum seekers – something Hungary, along with the Czech Republic, Poland and Slovakia, has rejected.
Hungary has become a major transit nation for people fleeing the Middle East and Africa, and seeking to reach north and west Europe.
The Hungarian parliament on September 4 approved tougher border controls and penalties for migrants, underlining divisions within the EU on how to tackle the crisis.
Hungary’s PM Viktor Orban has said the surge in arrivals was “Germany’s problem”, since that was where most people wanted to go.
However, Chancellor Angela Merkel has called for refugees to be fairly divided among EU members.
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