The intractability of homogeneous α-satellite arrays has impeded understanding of human centromeres. Artificial centromeres are produced from higher-order repeats (HORs) present at centromere edges, although the exact sequences and chromatin conformations of centromere cores remain unknown. We use high-resolution chromatin immunoprecipitation (ChIP) of centromere components followed by clustering of sequence data as an unbiased approach to identify functional centromere sequences. We find that specific dimeric α-satellite units shared by multiple individuals dominate functional human centromeres. We identify two recently homogenized α-satellite dimers that are occupied by precisely positioned CENP-A (cenH3) nucleosomes with two ~100-base pair (bp) DNA wraps in tandem separated by a CENP-B/CENP-C-containing linker, whereas pericentromeric HORs show diffuse positioning. Precise positioning is largely maintained, whereas abundance decreases exponentially with divergence, which suggests that young α-satellite dimers with paired ~100-bp particles mediate evolution of functional human centromeres. Our unbiased strategy for identifying functional centromeric sequences should be generally applicable to tandem repeat arrays that dominate the centromeres of most eukaryotes.