Centromeres direct the assembly of kinetochores, microtubule-attachment sites that allow chromosome segregation on the mitotic spindle. Fundamental differences in size and organization between evolutionarily distant eukaryotic centromeres have in many cases obscured general principles of their function. Here we demonstrate that centromere-binding proteins are highly conserved between budding yeast and humans. We identify the histone-fold protein Cnn1(CENP-T) as a direct centromere receptor of the microtubule-binding Ndc80 complex. The amino terminus of Cnn1 contains a conserved peptide motif that mediates stoichiometric binding to the Spc24-25 domain of the Ndc80 complex. Consistent with the critical role of this interaction, artificial tethering of the Ndc80 complex through Cnn1 allows mini-chromosomes to segregate in the absence of a natural centromere. Our results reveal the molecular function of CENP-T proteins and demonstrate how the Ndc80 complex is anchored to centromeres in a manner that couples chromosome movement to spindle dynamics.