Tau is a hallmark pathology of Alzheimer’s disease, and animal models have suggested that tau spreads from cell to cell through neuronal connections, facilitated by β-amyloid (Aβ). We test this hypothesis in humans using an epidemic spreading model (ESM) to simulate tau spread, and compare these simulations to observed patterns measured using tau-PET in 312 individuals along Alzheimer’s disease continuum. Up to 70% of the variance in the overall spatial pattern of tau can be explained by our model. Surprisingly, the ESM predicts the spatial patterns of tau irrespective of whether brain Aβ is present, but regions with greater Aβ burden show greater tau than predicted by connectivity patterns, suggesting a role of Aβ in accelerating tau spread. Altogether, our results provide evidence in humans that tau spreads through neuronal communication pathways even in normal aging, and that this process is accelerated by the presence of brain Aβ.