Segments of proteins with high β-strand propensity can self-associate to form amyloid fibrils implicated in many diseases. We describe a general approach to bind such segments in β-strand and β-hairpin conformations using de novo designed scaffolds that contain deep peptide-binding clefts. The designs bind their cognate peptides in vitro with nanomolar affinities. The crystal structure of a designed protein−peptide complex is close to the design model, and NMR characterization reveals how the peptide-binding cleft is protected in the apo state. We use the approach to design binders to the amyloid-forming proteins transthyretin, tau, serum amyloid A1 and amyloid β1−42 (Aβ42). The Aβ binders block the assembly of Aβ fibrils as effectively as the most potent of the clinically tested antibodies to date and protect cells from toxic Aβ42 species.