AP
The 62-year-old Müller was CEO of Porsche, which is among VW Group's brands. Müller's appointment comes as VW reels from an emissions-cheating scandal that has affected 11 million vehicles worldwide.
"My most urgent task is to win back trust for the Volkswagen Group - by leaving no stone unturned and with maximum transparency, as well as drawing the right conclusions from the current situation," Müller said in a statement.
"Under my leadership, Volkswagen will do everything it can to develop and implement the most stringent compliance and governance standards in our industry. If we manage to achieve that then the Volkswagen Group with its innovative strength, its strong brands and above all its competent and highly motivated team has the opportunity to emerge from this crisis stronger than before."
The VW supervisory board met Friday to vote on Müller's candidacy. Made up of members of VW Group management, labor leaders, representatives of the Porsche family, and the government of Lower Saxony, where VW is headquartered, the supervisory board has moved swiftly to deal with the scandal since the news broke last week.
Former CEO Martin Winterkorn, who had survived a management crisis earlier this year, resigned on Tuesday.
Bernd Osterloh, who leads the VW Group Works Council, the automaker's union, said in a statement that, "when it comes to leadership appointments the Volkswagen Group does not need hasty decisions.
He added: "We know and value Matthias Müller for his determination and decisiveness. He does not work on his own, rather he is a team player. That is what Volkswagen needs now."
Müller has been with the VW Group for decades. He began his career in the German auto industry in the 1970s, as an apprentice before going to college, and then rose through the ranks. He has presided over Porsche's transformation from a maker of expensive sports cars to a company that sells luxury SUV and sedans in both the developed and developing world.
Müller also has the support of former VW chairman Ferdinand Piëch, who was ousted from the VW board earlier this year, but continues to exert influence. During VW's management crisis, Müller was suggested as a CEO to replace Winterkorn, who was under fire for VW's weak performance in the US and its sprawling worldwide growth.
Various media reports has also noted that Müller was supported by both the Porsche family (of which Piëch is a member) and VW's powerful labor unions.
Additional VW executives, including its US leadership, were also slated to be dismissed. When we have details on that, we'll update.