German members of the public applauded and offered sweets as some 450 migrants arrived on a special train service.
The plight of the migrants has highlighted the EU's struggle to deal with a surge of asylum seekers
Earlier this week there were chaotic scenes in Budapest as Hungary blocked them from travelling onwards.
Many migrants refused to be taken to camps in Hungary to register for asylum, insisting they wanted to travel on to Germany and Austria.
Crowds broke through security lines and began walking 175km (108 miles) to the border, many with small children.
Under mounting pressure, Hungary opened its border with Austria, which expects to have received some 10,000 people by the end of Saturday.
Chancellor Angela Merkel has said Germany can cope with an influx of newcomers, without raising taxes or jeopardising its budget while Austria has said it will not limit the number of migrants crossing its borders.
There is however little sign of a co-ordinated EU response to the crisis, despite more than 350,000 migrants having crossed the EU's borders in 2015 alone.
Europe's migrant crisis is "here to stay" and nations must act together to deal with it effectively, the EU's foreign policy chief said after "difficult" talks with foreign ministers in Luxembourg.
"In three months time, it will be other member states under the focus, and in six months, it could be again others," Federica Mogherini said.
