He succeeded in preventing a collapse of sales and profits. But Mr. Müller, who has spent his entire career at Volkswagen or its subsidiaries, struggled to deliver on his promise to remake the company’s insular culture. The carmaker has continued to suffer blows to its reputation, including revelations in January that it had financed tests on monkeys in a bungled attempt to show that diesel exhaust was not as dangerous as it once was.
Mr. Diess, 59, carries less baggage than Mr. Müller because he arrived at Volkswagen only a few months before the diesel deceit erupted. And Mr. Diess has led Volkswagen’s push to mass produce electric cars, which are seen as essential to the company’s ability to defend itself against challengers like Tesla, Uber and Google that are trying to upend the auto industry.
“This is a chance for Volkswagen to make a change,” said Christian Strenger, the former chief executive of Deutsche Bank’s wealth management division, who is suing Volkswagen because he said it violated its duty to shareholders by failing to be forthcoming about the emissions scandal. But Mr. Strenger said that Mr. Diess would have to “have the guts to clean things up.”
Volkswagen is still the target of a wide-ranging criminal investigation that has included searches of Mr. Müller’s offices. However, there has been no new information that would have prompted Mr. Müller to leave now, said Klaus Ziehe, a spokesman for the prosecutors in Braunschweig who are conducting the inquiry.
German prosecutors have not charged anyone in the Volkswagen case, but they expect to complete their investigation this year. Two former Volkswagen executives, James Liang and Oliver Schmidt, are serving prison sentences in the United States after pleading guilty to charges including conspiracy to violate the Clean Air Act.
Mr. Müller was a high-ranking executive involved in product development at the same time that the company was developing the illegal software and deploying it in vehicles. He also worked closely with some of the people under investigation over possible involvement in the emissions scandal. Mr. Müller has insisted he was ignorant of any wrongdoing, but he has nonetheless faced the accusation that he was part of a system that allowed it to take place.
In a statement on Tuesday, Volkswagen said it was considering “a further development of the management structure of the group,” which could “include a change in the position of the chairman of the board of management,” referring to Mr. Müller. The company said it had not yet made a decision on him, but merely calling his status into question effectively sealed his fate.
Mr. Diess has a shorter history at Volkswagen than most other members of the management board, but he would nonetheless satisfy the company’s longtime preference for choosing chief executives from within its own ranks. He joined Volkswagen in July 2015 from BMW, where he had been a member of the management board in charge of product development. He has succeeded in improving the profitability of the division that makes Volkswagen brand cars like the Golf, Jetta and Passat. The division accounts for most of the cars that Volkswagen sells but is far less profitable than the company’s Audi and Porsche luxury brands.
Mr. Diess, who managed factories in Britain for BMW, is much more comfortable speaking English than Mr. Müller and will have an easier time communicating with investors and media outside Germany. Mr. Diess has also not spent his career steeped in Volkswagen culture and may be in a better position to change it.
But he will most likely face resistance from entrenched interests within the company. He has already clashed with Volkswagen’s powerful workers council, which has de facto veto power over major decisions.
And Mr. Diess must answer to Hans Dieter Pötsch, the chairman of the supervisory board and former chief financial officer of Volkswagen. Mr. Pötsch is a confidant of the Porsche family, which via a holding company owns more than half of Volkswagen’s shares. The family, descendants of the man who created the Volkswagen Beetle for Adolf Hitler, has been criticized by shareholders for failing to appoint more independent members of the supervisory board and resisting more sweeping change.
The challenges that Mr. Diess faces are considerable. Even now, the diesel scandal continues to corrode Volkswagen’s reputation.
In January, The New York Times reported that the company had helped to finance experiments in which monkeys were forced to breathe diesel fumes at a lab in Albuquerque. The exposure of the research caused a furor in Germany and beyond. Chancellor Angela Merkel condemned the experiments, the German Parliament debated possible consequences, and animal rights activists demonstrated outside Volkswagen’s headquarters in Wolfsburg.
Volkswagen’s cheating has also had an effect on the wider industry. Diesel was once the most popular engine option in Europe because of its fuel economy. But diesel vehicle sales have been dropping since Volkswagen’s deception was uncovered.
The scandal exposed the degree to which virtually all of the European carmakers took advantage of regulatory loopholes to sell diesels that polluted far more in everyday use than in official tests, causing poor air quality that led to thousands of premature deaths. As a result, cities across Europe have taken steps to restrict the use of diesel vehicles in urban centers. German carmakers have suffered the most from the backlash because of their dependence on the technology.
Volkswagen’s stock price closed the day 3.1 percent higher, at 169 euros, or about $208, on the news of Mr. Müller’s upcoming departure.