After starting his career in karting in 2004, Müller made the step up to single seaters in 2008 with Formula Renault. Here, the young Swiss driver placed first in the 2009 Swiss Formula Renault competition with Jenzer Motorsport after scoring a podium finish in each of the 12 races.
In 2010, Müller graduated to GP3, continuing his relationship with Jenzer. He took his first victory in the category at the third round of the season in Valencia before finishing the season third overall behind Robert Wickens and eventual champion Esteban Gutierrez.
In 2014, Müller added the German DTM series to his racing portfolio after securing a drive with Audi Sport Team Rosberg, a series in which he has remained in ever since. Between 2014 and his entry into Formula E, Müller has enjoyed a varied racing career, splitting his time between DTM, Rallycross, GT and Stock Car racing.
Ahead of the 2017/18 season, Müller took up testing and reserve duties for Audi Sport ABT Schaeffler, making his Formula E debut in the official rookie test in Marrakesh in January 2018. Topping the timesheets during the session, Müller went on to repeat the feat at the same test the following year.
Stepping up to a full-time drive for Dragon’s 2018/19 campaign, Müller joined fellow rookie Brendon Hartley for the team's sixth campaign in the series, competing until the Berlin E-Prix. The following campaign, he completed a half-season with the outfit, scoring a high of second spot in Valencia for his first podium and silverware in Formula E.