Police, firefighters and several armed response teams (SEK) had rushed to the scene and evacuated surrounding homes and a nearby school.
But Cologne police told The Local that the man had been arrested just after 3 pm.
A police spokeswoman police earlier said the man had made the threats following a family falling-out.
He is known to the police from previous drug offences, she added.
It is not known whether there was anyone else with him in the flat. The rest of the building had been evacuated.
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Gas and electricity supplies to the building were both cut off as a precautionary measure.