Human telomeres contain the repeat DNA sequence 5’(TTAGGG), with duplex regions that are several kilobases long terminating in a 3’ single-stranded overhang. The structure of the single-stranded overhang is not known with certainty, with disparate modes proposed in the literature. We report here the results of an integrated structural biology approach that combines small-angle X-ray scattering, circular dichroism (CD), analytical ultracentrifugation, size-exclusion column chromatography and molecular dynamics simulations that provide the most detailed characterization to date of the structure of the telomeric overhang. We find that the single-stranded sequences 5’(TTAGGG)n, with n=8, 12, and 16, fold into multimeric structures containing the maximal number (2, 3, and 4, respectively) of contiguous G4 units with no long gaps between units. The G4 units are a mixture of hybrid-1 and hybrid-2 conformers. In the multimeric structures, G4 units interact, at least transiently, at the interfaces between units to produce distinctive CD signatures. Global fitting of our hydrodynamic and scattering data to a worm-like chain (WLC) model indicates that these multimeric G4 structures are semi-flexible, with a persistence length of about 34 Å. Investigations of its flexibility using MD simulations reveal stacking, unstacking, and coiling movements, which yield unique sites for drug targeting.