Zellmer, currently serving as sales, marketing and aftersales boss of the Volkswagen brand, joined Porsche in 1999, leaving for a six-year stint at Daimler in 2004 before returning to Porsche as chief marketing officer.
His most recent position at the sports car brand was as president and CEO of Porsche Cars North America, a role he left in 2020 for his latest job at Volkswagen.
His appointment as boss of Skoda comes as chairman and COO Schäfer leaves at the end of June to head up the Volkswagen brand, taking over from Ralf Brandstätter, who will now oversee the Volkswagen Group's Chinese operations.
Zellmer will be larger with leading Skoda's ambitious Next Level transformation strategy, under which it will expand its line-up of electric cars, reduce its fleet emissions and dramatically revamp its design language.
As early as September, Skoda will launch a whole new brand identity called Modern Solid, which it describes as "the most dramatic change" for the brand since it joined the Volkswagen Group in 1994.
Murat Aksel, interim chairman of the Skoda board, said: "I'm delighted that we have been able to recruit one of our most high-profile managers to Skoda Auto.
"Klaus Zellmer has more than 20 years’ experience in the industry. During this time, he has not only distinguished himself as a leading automotive expert but has also demonstrated great strategic and entrepreneurial foresight.
"I'm convinced that, alongside the board team, he will do everything in his power to continue to systematically advance Skoda Auto’s successful development."