Kinetochores are macromolecular machines that couple chromosomes to dynamic microtubule tips during cell division, thereby generating force to segregate the chromosomes. Accurate segregation depends on selective stabilization of correct 'bi-oriented' kinetochore-microtubule attachments, which come under tension as the result of opposing forces exerted by microtubules. Tension is thought to stabilize these bi-oriented attachments indirectly, by suppressing the destabilizing activity of a kinase, Aurora B. However, a complete mechanistic understanding of the role of tension requires reconstitution of kinetochore-microtubule attachments for biochemical and biophysical analyses in vitro. Here we show that native kinetochore particles retaining the majority of kinetochore proteins can be purified from budding yeast and used to reconstitute dynamic microtubule attachments. Individual kinetochore particles maintain load-bearing associations with assembling and disassembling ends of single microtubules for >30 min, providing a close match to the persistent coupling seen in vivo between budding yeast kinetochores and single microtubules. Moreover, tension increases the lifetimes of the reconstituted attachments directly, through a catch bond-like mechanism that does not require Aurora B. On the basis of these findings, we propose that tension selectively stabilizes proper kinetochore-microtubule attachments in vivo through a combination of direct mechanical stabilization and tension-dependent phosphoregulation.