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.

He then graduated to a full-time drive for Dragon’s 2018/19 campaign, joining 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.

After sitting out for Season 8, the Thun-born driver rejoined the grid in Season 9 with the newly re-entered ABT Cupra for the start of the GEN3 era. It was a disappointing return to the sport for Müller and ABT Cupra, spending most of the season outside the points, as the team limped to a last-place finish.

Season 10 has seen Müller stick with ABT Cupra, with Robin Frijns being replaced by Lucas di Grassi for the German outfit. While he and ABT Cupra have struggled to get up to speed this season, he has come close to the podium, with a season-best of P4 in Round 7 in Misano, at the time of writing.