A critical structure poised to coordinate chromosome segregation with division plane specification is the central spindle that forms between separating chromosomes after anaphase onset. The central spindle acts as a signalling centre that concentrates proteins essential for division plane specification and contractile ring constriction. However, the molecular mechanisms that control the initial stages of central spindle assembly remain elusive. Using Caenorhabditis elegans zygotes, we found that the microtubule-bundling protein SPD-1(PRC1) and the motor ZEN-4(MKLP-1) are required for proper central spindle structure during its elongation. In contrast, we found that the kinetochore controls the initiation of central spindle assembly. Specifically, central spindle microtubule assembly is dependent on kinetochore recruitment of the scaffold protein KNL-1, as well as downstream partners BUB-1, HCP-1/2(CENP-F) and CLS-2(CLASP); and is negatively regulated by kinetochore-associated protein phosphatase 1 activity. This in turn promotes central spindle localization of CLS-2(CLASP) and initial central spindle microtubule assembly through its microtubule polymerase activity. Together, our results reveal an unexpected role for a conserved kinetochore protein network in coupling two critical events of cell division: chromosome segregation and cytokinesis.