There have been attempts in the past to fit the observed bulk shapes (axial ratios) of asteroids to theoretical equilibrium figures for fluids, but these attempts have not been successful in many cases, evidently because asteroids are not fluid bodies. So far, however, the observed distribution of asteroid macroscopic shapes has never been attributed to a common cause. Here, we show that a general mechanism exists, capable of producing the observed shape distribution. We base our approach on the idea that aggregates of coherent blocks held together mostly by gravity (gravitational aggregates) can change their shape under the action of external factors, such as minor collisions, that break the interlocking of the constituent blocks, thus allowing them to asymptotically evolve toward fluid equilibrium. We show by numerical simulations that this behavior can produce a shape distribution compatible with the observations. Our results are shown to be consistent with a simple interpretation based on the topology of the potential energy field for rotating bodies. Also, they suggest that most asteroids have an internal structure that is at least partially fragmented, consistent with constraints derived from large asteroids (diameters >100 km) with satellites.