Cytokinesis controls the proper segregation of nuclear and cytoplasmic materials at the end of cell division. The chromosomal passenger complex (CPC) has been proposed to monitor the final separation of the two daughter cells at the end of cytokinesis in order to prevent cell abscission in the presence of DNA at the cleavage site, but the precise molecular basis for this is unclear. Recent studies indicate that abscission could be mediated by the assembly of filaments comprising components of the endosomal sorting complex required for transport-III (ESCRT-III). Here, we show that the CPC subunit Borealin interacts directly with the Snf7 components of ESCRT-III in both Drosophila and human cells. Moreover, we find that the CPC's catalytic subunit, Aurora B kinase, phosphorylates one of the three human Snf7 paralogues—CHMP4C—in its C-terminal tail, a region known to regulate its ability to form polymers and associate with membranes. Phosphorylation at these sites appears essential for CHMP4C function because their mutation leads to cytokinesis defects. We propose that CPC controls abscission timing through inhibition of ESCRT-III Snf7 polymerization and membrane association using two concurrent mechanisms: interaction of its Borealin component with Snf7 proteins and phosphorylation of CHMP4C by Aurora B.