Behaviour requires distributed neural processing to be flexibly integrated and segregated, which in turn demands that information be dynamically routed across the brain. However, whether a unifying principle governs the routing of neural activity remains unknown. Here, we report that the flow of cortical activity is directed through canonical routing modes that are conserved across individuals, robust to variations in age, frequency band, brain state, and even the presence of neurodegeneration. These modes are constructed from the divergence and vorticity of the time-varying unit-phase vector field derived from electroencephalogram (EEG) recordings. We show that the canonical routing modes are flexibly combined to generate distinct, state- and function-dependent flow architectures that remain consistent across individuals. Disruption to the routing mode dynamics mechanistically links structural abnormalities and cognitive impairment in Alzheimer's disease. Together, these canonical routing modes provide a unified framework for describing, modelling, and predicting the dynamic integration and segregation of macroscopic brain activity underpinning behaviour.