In 1993, he joined forces with Willi Weber, which initially led him to run the WTS Formula Three team.

Tost followed him, working for Williams' engine supplier BMW as Track Operations Manager until 1 January 2006.

[2] He retained the role of team principal when Toro Rosso were re-christened as AlphaTauri at the beginning of the 2020 season.

Following the 2007 European Grand Prix, at the Nürburgring in Germany, it was alleged that Tost assaulted driver Scott Speed over an incident on the track.

After Tost later denied the incident, Speed went to the press describing the acrimonious situation at the team, stating that "after coming out and denying this stuff, it's just another very dishonest thing that Franz or Gerhard [Berger] have said in the media to damage me and Tonio (Vitantonio Liuzzi)".