The "dieselgate" scandal - in which VW admitted to installing software in 11 million diesel vehicles worldwide to cheat regulatory emissions test - has so far cost it more than 25 billion euros ($31 billion) in buybacks, fines and compensation.
Warburton said, however, that despite fears that Volkswagen's insular culture might reject Diess's hardnosed approach, "instead of being squeezed out he has been pushed upward and made CEO", calling that "a sign of real change at VW".
Newly named Volkswagen CEO Herbert Diess (center) speaks at a technology conference in Germany previous year.
Chairman of the Supervisory Board Hans Dieter Petch thanked Mueller and called his work "outstanding".
The "volume" business includes the VW brand, Seat and Skoda.
"Diess is a man of action, he is the most plausible choice at VW to lead the group into the next phase of its transformation", said Nord LB analyst Frank Schwope.
German business newspaper Handelsblatt and national news agency DPA had all tipped Diess, head of the VW brand, as Mueller's successor.
Even as Volkswagen has been moving to implement its Strategy 2025, the automaker has played some chess with its top executives, moving Herbert Diess, its brand chief, up to the top spot.
Mr. Mueller had been running Porsche before being lifted to supplant Martin Winterkorn as VW boss.
"The group has fundamentally realigned and repositioned itself for it 2025 strategy".
Europe's largest automotive group is poised to replace group chief executiveMatthias Mueller this week with Diess, a cost-cutter hired in 2015 from BMW as it seeks fresh impetus for its recovery from an emissions scandal.
Separately, VW said it is preparing its truck and bus division for the capital markets, a step that could include selling shares in the division.
The appointment of Diess comes as VW investors are demanding for increased profitability.
And the chief executive of Porsche, Oliver Blume, will join the main VW board. Mueller had been tapped as CEO unexpectedly in September 2015 when Martin Winterkorn resigned over the scandal in which the company had rigged carts to cheat on U.S. emissions tests.
The automaker also moved to replace its human resources director, Karlheinz Blessing, with Gunnar Kilian.
Diess acknowledged the change would allow managers to make quicker selections on pricing, promoting and advertising and product sales.