During vertebrate mitosis, the centromere-associated kinesin CENP-E (centromere protein E) transports misaligned chromosomes to the plus ends of spindle microtubules. Subsequently, the kinetochores that form at the centromeres establish stable associations with microtubule ends, which assemble and disassemble dynamically. Here we provide evidence that after chromosomes have congressed and bi-oriented, the CENP-E motor continues to play an active role at kinetochores, enhancing their links with dynamic microtubule ends. Using a combination of single-molecule approaches and laser trapping in vitro, we demonstrate that once reaching microtubule ends, CENP-E converts from a lateral transporter into a microtubule tip-tracker that maintains association with both assembling and disassembling microtubule tips. Computational modelling of this behaviour supports our proposal that CENP-E tip-tracks bi-directionally through a tethered motor mechanism, which relies on both the motor and tail domains of CENP-E. Our results provide a molecular framework for the contribution of CENP-E to the stability of attachments between kinetochores and dynamic microtubule ends.