His work consists mainly of narrative prose, which often has a penchant for political satire or features tragicomic elements. His first published books include Briefe aus Amerika (1998), a postmodern novel which playfully overdraws the clichés of America, as well as Die Würde des Lügens (2000), a novel which explores the ambiguities of truth and fiction. Further book publications include Schule der Arbeitslosen (2006), a dystopian novel about a boot camp drilling unemployed people, Der Ministerpräsident (2010) and untertan (2012), an adaptation of Heinrich Mann’s classic The Loyal Subject.
In recent years, Zelter has written stage adaptations of his prose, as well as theatre plays that were performed on stages in Germany and Austria. He has received many awards for his literary work, among which a scholarship from the federal state Baden-Württemberg in 2005, and a nomination for the German Book Prize in 2010 for his novel Der Ministerpräsident. His books were translated into numerous languages.