To ensure equal chromosome segregation during mitosis, the macromolecular kinetochore must remain attached to depolymerizing microtubules, which drive chromosome movements. How kinetochores associate with depolymerizing microtubules, which undergo dramatic structural changes forming curved protofilaments, has yet to be defined in vertebrates. Here, we demonstrate that the conserved kinetochore-localized Ska1 complex tracks with depolymerizing microtubule ends and associates with both the microtubule lattice and curved protofilaments. In contrast, the Ndc80 complex, a central player in the kinetochore-microtubule interface, binds only to the straight microtubule lattice and lacks tracking activity. We demonstrate that the Ska1 complex imparts its tracking capability to the Ndc80 complex. Finally, we present a structure of the Ska1 microtubule binding domain that reveals its interaction with microtubules and its regulation by Aurora B. This work defines an integrated kinetochore-microtubule interface formed by the Ska1 and Ndc80 complexes that associates with depolymerizing microtubules, potentially by interacting with curved microtubule protofilaments.