Rüdorff was born in Berlin in 1909. He studied chemistry as an undergraduate at Technical University of Berlin and graduated in 1925. His graduate study was carried out under the supervision of Ulrich Hofmann at the same university, where he graduated with a PhD thesis titled Über die Kristallstruktur der Hexacarbonyle von Chrom, Molybdän und Wolfram. He then moved to the University of Rostock along with Ulrich Hofmann and achieved his habilitation status with the thesis titled Neuartige Verbindungen mit Graphit in 1941. In 1942, Rüdorff moved to Technical University of Vienna following Ulrich Hofmann. He later took up a faculty position at University of Tübingen in 1947. He stayed in Tübingen until his retirement.
Along with his supervisor Ulrich Hofmann and his father Karl Andreas Hofmann, Rüdorff cowrote the famous textbook on inorganic chemistry that are referred to as Rüdorff-Hofmann.