The man, who is in his mid-20s and appears to come from somewhere in Eastern Europe, was found in an industrial area in the east of Oslo in what police described as "a bad condition".
He speaks very good English with an east European accent, understands Czech, Slovak, Polish and Russian, and is calling himself "John Smith" until he recovers memories of his real name.
"The man has no identity papers, and does not remember his name, where he came from, how he ended up in Norway or any other details of his life," the police wrote in their statement.
Oslo police have tried to establish the man's identity for nearly four months, sending photos and fingerprints to East European police forces via Interpol, and searching through lists of missing people.
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"We have come to a point in the investigation where we had tried everything without getting anywhere," Sturla Henriksbø from the Oslo police told VG newspaper. "Therefore we are now, in consultation with the man himself, releasing his picture."
See update: Man with no memory was bound and drugged