Error-free mitosis depends on accurate chromosome attachment to spindle microtubules, powered congression of those chromosomes, their segregation in anaphase, and assembly of a spindle midzone at mitotic exit. The centromere-associated kinesin motor CENP-E, whose binding partner is BubR1, has been implicated in congression of misaligned chromosomes and the transition from lateral kinetochore-microtubule association to end-on capture. Although previously proposed to be a pseudokinase, here we report the structure of the kinase domain of Drosophila melanogaster BubR1, revealing its folding into a conformation predicted to be catalytically active. BubR1 is shown to be a bona fide kinase whose phosphorylation of CENP-E switches it from a laterally attached microtubule motor to a plus-end microtubule tip tracker. Computational modeling is used to identify bubristatin as a selective BubR1 kinase antagonist that targets the αN1 helix of N-terminal extension and αC helix of the BubR1 kinase domain. Inhibition of CENP-E phosphorylation is shown to prevent proper microtubule capture at kinetochores and, surprisingly, proper assembly of the central spindle at mitotic exit. Thus, BubR1-mediated CENP-E phosphorylation produces a temporal switch that enables transition from lateral to end-on microtubule capture and organization of microtubules into stable midzone arrays.