Shelterin is a six-subunit protein complex that plays crucial roles in telomere length regulation, protection, and maintenance. Although several shelterin subunits have been studied in vitro, the biochemical properties of the fully assembled shelterin complex are not well defined. Here, we characterize shelterin using ensemble biochemical methods, electron microscopy, and single-molecule imaging to determine how shelterin recognizes and assembles onto telomeric repeats. We show that shelterin complexes can exist in solution and primarily locate telomeric DNA through a three-dimensional diffusive search. Shelterin can diffuse along non-telomeric DNA but is impeded by nucleosomes, arguing against extensive one-dimensional diffusion as a viable assembly mechanism. Our work supports a model in which individual shelterin complexes rapidly bind to telomeric repeats as independent functional units, which do not alter the DNA-binding mode of neighboring complexes but, rather, occupy telomeric DNA in a "beads on a string" configuration.