Impact craters are the most obvious indication of asteroid impacts, but craters on Earth are quickly obscured or destroyed by surface weathering and tectonic processes. Earth’s impact history is inferred therefore either from estimates of the present-day impactor flux as determined by observations of near-Earth asteroids, or from the Moon’s incomplete impact chronology. Asteroids hitting Earth typically vaporize a mass of target rock comparable to the projectile’s mass. As this vapour expands in a large plume or fireball, it cools and condenses into molten droplets called spherules. For asteroids larger than about ten kilometres in diameter, these spherules are deposited in a global layer. Spherule layers preserved in the geologic record accordingly provide information about an impact even when the source crater cannot be found. Here we report estimates of the sizes and impact velocities of the asteroids that created global spherule layers. The impact chronology from these spherule layers reveals that the impactor flux was significantly higher 3.5 billion years ago than it is now. This conclusion is consistent with a gradual decline of the impactor flux after the Late Heavy Bombardment.