Kjell Gruner, 53, will take over as CEO of Porsche Cars North America. Gruner is Porsche's chief marketing officer and global vice president of marketing.
Zellmer's appointment is the latest in a number of changes at VW in recent months.
Zellmer has been with Porsche for 23 years. He rose through the sales ranks in France and Germany. He was appointed CEO of Porsche's North American business in 2015 and since then has boosted sales in the key U.S. market by 4.4 percent annually.
"Together with him, we will systematically continue to pursue the course set by New Volkswagen," Brandstätter said in a statement, referring to the new push into electric vehicles with models such as the ID3 hatchback and the upcoming ID4 crossover.