Katzberg, 22, who cuts a distinctive figure with his moustache and long curly hair, asserted himself with a first throw of 84.12 metres, and none of his rivals could respond.
Hungary's Bence Halasz won silver with 79.97 and Ukraine's Mykhaylo Kokhan won bronze with 79.39.
It was a changing of the guard as defending Olympic champion, Poland's Wojciech Nowicki, 35, finished seventh and his teammate, Tokyo bronze medallist Pawel Fajdek, was fifth, taking a bow after his final throw.
Norway's Eivind Henriksen, who won silver in Tokyo, was fourth.