The court in Lower Saxony cleared the way for the debt-ridden hotel's receiver to evict the neo-Nazis, who had been occupying the premises amid a tense standoff with police and local anti-Nazi protesters.
Hours before the decision, German commandos had raided the hotel after hearing what they thought to be gunshots.
They found several fake firearms, a concealable truncheon and pepper spray. Twelve neo-Nazis were on the premises, four of whom were minors and were handed over to youth services.
Late on Tuesday, the eight remaining neo-Nazis, masked and hooded, left the premises peacefully after police moved in, a police spokesman said.
One day before they went into receivership, the owners of the hotel had signed a 10-year lease with Jürgen Rieger, a Hamburg lawyer, holocaust denier and senior member of the far-right National Democratic Party.
When the receiver, Jens Wilhelm, tried to order Rieger's supporters off the premises in mid-July, a group of them stormed the building and refused to leave.
During the volatile standoff that followed, shots were fired in the surrounding area and police confiscated weapons from the Nazis and from leftist counter-demonstrators.
Rieger, who has a lengthy criminal record for Holocaust denial and other crimes, sparked fury in Germany with his plan for the training centre, which evoked painful memories of the "Hitler Youth" during the Third Reich.
The court decision came as the far-right Collegium Humanum organisation prepared to appeal to the federal court on Wednesday to have its ban overturned.
Germany's Interior Ministry outlawed the 46-year-old group last year on the grounds that it opposed the German constitution, denied the Holocaust and glorified National Socialism.
