The paired helical filaments (PHF) formed by the intrinsically disordered human protein tau are one of the pathological hallmarks of Alzheimer disease. PHF are fibers of amyloid nature that are composed of a rigid core and an unstructured fuzzy coat. The mechanisms of fiber formation, in particular the role that hydration water might play, remain poorly understood. We combined protein deuteration, neutron scattering, and all-atom molecular dynamics simulations to study the dynamics of hydration water at the surface of fibers formed by the full-length human protein htau40. In comparison with monomeric tau, hydration water on the surface of tau fibers is more mobile, as evidenced by an increased fraction of translationally diffusing water molecules, a higher diffusion coefficient, and increased mean-squared displacements in neutron scattering experiments. Fibers formed by the hexapeptide (306)VQIVYK(311) were taken as a model for the tau fiber core and studied by molecular dynamics simulations, revealing that hydration water dynamics around the core domain is significantly reduced after fiber formation. Thus, an increase in water dynamics around the fuzzy coat is proposed to be at the origin of the experimentally observed increase in hydration water dynamics around the entire tau fiber. The observed increase in hydration water dynamics is suggested to promote fiber formation through entropic effects. Detection of the enhanced hydration water mobility around tau fibers is conjectured to potentially contribute to the early diagnosis of Alzheimer patients by diffusion MRI.