Chromosome segregation depends on a regulated connection between spindle microtubules and centromeric DNA. The kinetochore, a massive modular protein assembly, mediates this connection and also serves as a signaling hub that integrates and responds to changing cues during the cell cycle. Kinetochore functions evolve as the cell cycle progresses, culminating in the assurance of a persistent chromosome-microtubule connection during anaphase, when sister chromatids must transit into daughter cells uninterrupted. We previously determined the structure of the Ctf19 complex, a group of kinetochore proteins at the centromeric base of the kinetochore. We now present a high-resolution structure of a Ctf19 complex sub-assembly involved in centromere-microtubule contact: the Ctf3 complex bound to the Cnn1-Wip1 heterodimer. The resulting composite model of the Ctf19 complex and live-cell imaging experiments provide a mechanism for Cnn1-Wip1 recruitment to the kinetochore. The mechanism suggests feedback regulation of Ctf19 complex assembly and unanticipated similarities in kinetochore organization between yeast and vertebrates.