As a young man, Tost competed in Formula Ford and Formula Three. He then studied Sport Science and Management, working as a team manager at the Walter Lechner Racing School. He joined Willi Weber Management in 1993. He initially ran the WTS Formula Three team, then looked after a young Ralf Schumacher's career in Japan. When the German moved into F1, Tost followed him, working for BMW as the German marque re-entered F1 in 2000 as engine supplier for the Williams team, for whom Schumacher was driving at the time. Tost worked for BMW as Track Operations Manager until 1 January 2006, when the new Scuderia Toro Rosso team hired him as Team Principal.
Following the 2007 European Grand Prix, at the Nürburgring in Germany, it was alleged that Tost assaulted driver Scott Speed after the first turn confusion caused by rain. 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 and Gerhard have said in the media to damage me and Tonio". Scott also stated that he doesn't want to race for Tost and Berger again.