"Due to the great cooperation of everyone involved, we can allow a humanitarian reception of the refugees at the Munich main railway station," the Munich police announced on Twitter.
Migrants have set up camps at the Keleti station in the Hungarian capital of Budapest on Tuesday after police prevented them from boarding trains traveling to Germany and other EU member states.
The closures were spurred by the arrival of 2,500 migrants in southern Germany the previous night.
Tensions and overcrowding led to protests throughout Wednesday, after which rail officials allowed those stranded at Keleti to travel onward.
Police later stopped a train near the Austrian border shortly after it left Budapest, subsequently letting an estimated 100 migrants back on board. Later media reports suggested that a batch of passengers from the intercepted train were taken to a nearby camp.
Hungarian Prime Minister Viktor Orban, whose efforts at stemming the migrant tide culminated in the construction of a fence at the Hungarian-Serbian border, later pledged to build another barrier at the Croatian border to cut off a potential alternative route.
Hungary, where an estimated 156,000 undocumented migrants have arrived this year, serves as a transit country for migrants hoping to reach more affluent EU member states and apply for asylum there.
