The first group of what are expected to be some 10,000 migrants has been greeted in Munich after an arduous journey through Hungary and Austria.
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
And Austria has said it will not limit the number of migrants crossing its borders, with an interior ministry spokesperson telling the BBC on Saturday that that the nation was dealing with an influx of people from “crisis regions” who were “desperate”.
However, there is 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.
Germany, backed by the European Commission, has been pushing for a quota system for dividing the people reaching Europe between member states. But this has been opposed by several eastern members.
On Saturday, Hungary said that while it had temporarily relaxed restrictions on the transit of asylum seekers, it was pressing ahead with plans to tighten border controls and could send troops to its southern frontier if parliament agreed.
However Ms Mogherini said she was still optimistic of progress.
“I do have hope – I always have hope – but I have to admit that the discussion also today was a difficult one. But again: no one has the illusion, and no one can have the illusion today that there is one single member state that is not concerned by this crisis.
“In three months time, it will be other member states under the focus, and in six months, it could be again others. We are all together in this, and the sooner we realise we have to take urgent decisions together – the better, and the [more] effective they will be.”
At the scene: Matthew Price, BBC News
Our correspondent has been walking with hundreds of migrants travelling on foot to Austria.
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