The appointment is a blow to Modem Media, which had been Hertz's European digital agency of record.
Fullsix, which already worked with Hertz in France out of its Paris office on a local basis, picked up the pan-European business following a final pitch against two other shortlisted agencies.
The process was overseen by Rhys Jarvis, head of online marketing and strategy at Hertz. According to Fullsix, the appointment reflects the car-hire company's desire to create more co-ordinated digital activity across Europe.
It has been tasked with developing Hertz's website as well as creating digital and email marketing campaigns.
The agency is already working with the company on developing its Hertz Number 1 Club loyalty scheme.
DDB London creates the advertising for Hertz, while DDB WWAV Rapp Collins handles the company's direct business.
Hertz, which claims to be the biggest car rental company in the world, launched its first website in 1996.
Last year, Hertz's rival Avis launched its first pan-European digital campaign, created by digital agency Profero.