The history of the Hadean Earth (∼4.0-4.5 billion years ago) is poorly understood because few known rocks are older than ∼3.8 billion years old. The main constraints from this era come from ancient submillimetre zircon grains. Some of these zircons date back to ∼4.4 billion years ago when the Moon, and presumably the Earth, was being pummelled by an enormous flux of extraterrestrial bodies. The magnitude and exact timing of these early terrestrial impacts, and their effects on crustal growth and evolution, are unknown. Here we provide a new bombardment model of the Hadean Earth that has been calibrated using existing lunar and terrestrial data. We find that the surface of the Hadean Earth was widely reprocessed by impacts through mixing and burial by impact-generated melt. This model may explain the age distribution of Hadean zircons and the absence of early terrestrial rocks. Existing oceans would have repeatedly boiled away into steam atmospheres as a result of large collisions as late as about 4 billion years ago.