An asteroid's history is determined in large part by its strength against collisions with other objects (impact strength). Laboratory experiments on centimetre-scale meteorites have been extrapolated and buttressed with numerical simulations to derive the impact strength at the asteroid scale . In situ evidence of impacts on boulders on airless planetary bodies has come from Apollo lunar samples and images of the asteroid (25143) Itokawa . It has not yet been possible, however, to assess directly the impact strength, and thus the absolute surface age, of the boulders that constitute the building blocks of a rubble-pile asteroid. Here we report an analysis of the size and depth of craters observed on boulders on the asteroid (101955) Bennu. We show that the impact strength of metre-sized boulders is 0.44 to 1.7 megapascals, which is low compared to that of solid terrestrial materials. We infer that Bennu's metre-sized boulders record its history of impact by millimetre- to centimetre-scale objects in near-Earth space. We conclude that this population of near-Earth impactors has a size frequency distribution similar to that of metre-scale bolides and originates from the asteroidal population. Our results indicate that Bennu has been dynamically decoupled from the main asteroid belt for 1.75 ± 0.75 million years.