He will succeed Thomas Schaefer, who joined the VW brand's board of management on April 1, initially as chief operating officer.
Schaefer will become VW brand CEO on July 1, succeeding Ralf Brandstaetter, who will take charge of VW Group's China operations in August. Schaefer's switch to the VW brand was announced in December.
In his new role, Schaefer will be head of VW Group's volume brand business, which comprises the VW passenger cars brand, Skoda and Seat/Cupra.
He will be tasked with preventing overlap between the VW Group's volume brands while finding more synergies.
Zellmer is not the first former Porsche executive to be placed in charge of Skoda. Bernhard Maier, a former head of Porsche's global sales and marketing, was Skoda CEO from 2015 to 2020.
VW said on Monday that Zellmer's successor as VW brand's sales and marketing chief will be announced at a later date.
Reuters contributed to this report