During cell division, spindle fibers attach to chromosomes at centromeres. The DNA sequence at regional centromeres is fast evolving with no conserved genetic signature for centromere identity. Instead CENH3, a centromere-specific histone H3 variant, is the epigenetic signature that specifies centromere location across both plant and animal kingdoms. Paradoxically, CENH3 is also adaptively evolving. An ongoing question is whether CENH3 evolution is driven by a functional relationship with the underlying DNA sequence. Here, we demonstrate that despite extensive protein sequence divergence, CENH3 histones from distant species assemble centromeres on the same underlying DNA sequence. We first characterized the organization and diversity of centromere repeats in wild-type Arabidopsis thaliana We show that A. thaliana CENH3-containing nucleosomes exhibit a strong preference for a unique subset of centromeric repeats. These sequences are largely missing from the genome assemblies and represent the youngest and most homogeneous class of repeats. Next, we tested the evolutionary specificity of this interaction in a background in which the native A. thaliana CENH3 is replaced with CENH3s from distant species. Strikingly, we find that CENH3 from Lepidium oleraceum and Zea mays, although specifying epigenetically weaker centromeres that result in genome elimination upon outcrossing, show a binding pattern on A. thaliana centromere repeats that is indistinguishable from the native CENH3. Our results demonstrate positional stability of a highly diverged CENH3 on independently evolved repeats, suggesting that the sequence specificity of centromeres is determined by a mechanism independent of CENH3.