Porsche said in a statement that its supervisory board appointed 47-year-old Blume, previously the board member in charge of production and logistics, at a meeting today.
Supervisory board chief Wolfgang Porsche said he was "particularly pleased" that Blume and Detlev von Platen, who was also appointed today to take charge of sales and marketing, were both company insiders.
"Porsche doesn't only have a highly motivated workforce, but also a very large number of qualified top managers," Porsche said.
Since then, he also worked at VW's Spanish unit SEAT and was head of production planning for the VW brand in 2009 before being appointed Porsche board member in 2013.
His predecessor Mueller, 62, headed Porsche for five years before he was named new CEO of the entire VW group last Friday, taking over from Martin Winterkorn who resigned in the wake of the global pollution-cheating scandal.
Board chief Porsche praised Mueller, saying the sports car maker had "practically doubled unit sales, turnover and the number of employees" under his reign.