The origin and dynamics of the Van Allen radiation belts is one of the longest-standing questions of the space age, and one that is increasingly important for space applications as satellite systems become more sophisticated, smaller and more susceptible to radiation effects. The precise mechanism by which the Earth's magnetosphere is able to accelerate electrons from thermal to ultrarelativistic energies (E0.5 MeV) has been particularly difficult to definitively resolve. The traditional explanation is that large-scale, fluctuating electric and magnetic fields energize particles through radial diffusion1. More recent theories2, 3 and observations4, 5 have suggested that gyro-resonant wave–particle interactions may be comparable to or more important than radial diffusion. Using data collected simultaneously by multiple satellites passing through the magnetosphere at different distances from the Earth, we demonstrate that the latter of these is the dominant mechanism responsible for relativistic electron acceleration. Specifically, we identify frequent and persistent peaks in equatorial electron phase space density near or inside geosynchronous orbit that provide unambiguous evidence for local wave–particle acceleration. These observations represent an important step towards a more complete physical understanding of radiation belt dynamics and to the development of space-weather models.