Müller, who ceded the top spot at the Volkswagen Group to Herbert Diess in 2018, will work alongside founders Piëch and Rea Stark to bring an electric two-seat sports car - based on last year’s Mark Zero concept - to production.
Müller said: “I was immediately enthusiastic about the mission of the two founders, because it's more compelling and more visionary than all the new approaches I have encountered during my work in the automotive industry.
“I'm proud to be involved in the business. It has the potential to herald a new chapter for modern mobility and shape the future of the automobile. It's an endeavour that will receive my wholehearted support.”
The finished car will feature “highly innovative battery technology and a record-low charging time”, according to the company. The concept, unlike similar propositions from rival start-ups, shuns the conventional ‘skateboard’ architecture in favour of a modular platform developed in collaboration with 200 external employees.
With centrally mounted batteries feeding a trio of electric motors, the Mark Zero is claimed to accelerate from 0-62mph in 3.2sec and hit a top speed of 155mph. A rapid charge to 80%, Piëch says, will take less than five minutes.
The production car is now said to be fully designed ahead of the first prototypes being built. It's set to become available to buy in 2022 with a claimed range of 310 miles.
Müller’s appointment comes as chief technology officer Klaus Schmidt, previously the chief engineer at BMW Motorsport, takes on the role of joint-CEO alongside chief marketing officer Andreas Henke, who used to work for Porsche.
Another recent recruit is head of sales Jochen Rudat, who reported directly to Tesla boss Elon Musk while building the EV maker's European dealership network over the course of 10 years.
In addition, Piëch has announced that it has completed its first round of of financing, during which tech billionaire Peter Thiel came aboard. The second round, which is required to bring the Mark Zero to production, will start in the next few months.
The company also plans to soon start construction on an engineering facility in Memmingen, Germany.