The driver, a 17-year-old woman from the Ashford area, and a 20-year-old man from the Maidstone area, who was in the passenger seat, were both pronounced dead at the scene.
The Maidstone-bound carriageway was closed until 2am today while officers investigated the collision and recovered the car.
Police would like to hear from anyone who witnessed the collision or may have seen the Fiesta in the area at the time.
The witness appeal line is 01622 798538.
More top news
Tuesday evening's weather for the east of the region
Tuesday evening's weather for the west of the region
Highways England thanked people for pointing it out. The A34 sign has now been removed.