Amyloid imaging by positron emission tomography (PET) is an important method for diagnosing neurodegenerative disorders such as Alzheimer's disease. Many 11C- and 18F-labeled PET tracers show varying binding capacities, specificities, and affinities for their target proteins. The structural basis of these variations is poorly understood. Here we employ 19F and 13C solid-state NMR to investigate the binding sites of a PET ligand, flutemetamol, to the 40-residue Alzheimer's β-amyloid peptide (Aβ40). Analytical high-performance liquid chromatography and 19F NMR spectra show that flutemetamol binds the current Aβ40 fibril polymorph with a stoichiometry of one ligand per four to five peptides. Half of the ligands are tightly bound while the other half are loosely bound. 13C and 15N chemical shifts indicate that this Aβ40 polymorph has an immobilized N-terminus, a non-β-sheet His14, and a non-β-sheet C-terminus. We measured the proximity of the ligand fluorine to peptide residues using 19F-13C and 19F-1H rotational-echo double-resonance (REDOR) experiments. The spectra show that three segments in the peptide, 12VHH14, 18VFF20, and 39VV40, lie the closest to the ligand. REDOR-constrained docking simulations indicate that these three segments form multiple binding sites, and the ligand orientations and positions at these sites are similar across different Aβ polymorphs. Comparison of the flutemetamol-interacting residues in Aβ40 with the small-molecule binding sites in other amyloid proteins suggest that conjugated aromatic compounds preferentially bind β-sheet surface grooves lined by aromatic, polar, and charged residues. These motifs may explain the specificity of different PET tracers to different amyloid proteins.