Bedrock erosion in rivers sets the pace of landscape evolution, influences the evolution of orogens and determines the size, shape and relief of mountains. A variety of models link fluid flow and sediment transport processes to bedrock incision in canyons. The model components that represent sediment transport processes are increasingly well developed. In contrast, the model components being used to represent fluid flow are largely untested because there are no observations of the flow structure in bedrock canyons. Here we present a 524-kilometre, continuous centreline, acoustic Doppler current profiler survey of the Fraser Canyon in western Canada, which includes 42 individual bedrock canyons. Our observations of three-dimensional flow structure reveal that, as water enters the canyons, a high-velocity core follows the bed surface, causing a velocity inversion (high velocities near the bed and low velocities at the surface). The plunging water then upwells along the canyon walls, resulting in counter-rotating, along-stream coherent flow structures that diverge near the bed. The resulting flow structure promotes deep scour in the bedrock channel floor and undercutting of the canyon walls. This provides a mechanism for channel widening and ensures that the base of the walls is swept clear of the debris that is often deposited there, keeping the walls nearly vertical. These observations reveal that the flow structure in bedrock canyons is more complex than assumed in the models presently used. Fluid flow models that capture the essence of the three-dimensional flow field, using simple phenomenological rules that are computationally tractable, are required to capture the dynamic coupling between flow, bedrock erosion and solid-Earth dynamics.