The assembly of tau into amyloid filaments is associated with more than twenty neurodegenerative diseases, collectively termed tauopathies. Cryo-EM structures of brain-derived tau filaments revealed that specific structures define different diseases, triggering a quest for the development of experimental model systems that replicate the structures of disease. Here, we describe twelve phosphomimetic, serine/threonine to aspartate, mutations in tau, which we termed PAD12, that collectively induce the in vitro assembly of full-length tau into filaments with the same structure as that of paired helical filaments extracted from the brains of individuals with Alzheimer's disease. Solution-state nuclear magnetic resonance spectroscopy suggests that phosphomimetic mutations in the carboxy-terminal domain of tau may facilitate filament formation by disrupting an intramolecular interaction between two IVYK motifs. PAD12 tau can be used for both nucleation-dependent and multiple rounds of seeded assembly in vitro, as well as for the seeding of tau biosensor cells. PAD12 tau can be assembled into paired helical filaments under various shaking conditions, with the resulting filaments being stable for extended periods of time. They can be labelled with fluorophores and biotin. Tau filaments extracted from the brains of individuals with Alzheimer's disease brains have been known to be made of hyperphosphorylated and abnormally phosphorylated full-length tau, but it was not known if the presence of this post-translational modification is more than a mere correlation. Our findings suggest that hyperphosphorylation of tau may be sufficient for the formation of the Alzheimer tau fold. PAD12 tau will be a useful tool for the study of molecular mechanisms of neurodegeneration.