Cohesin pairs sister chromatids by forming a tripartite Scc1-Smc1-Smc3 ring around them. In mitosis, cohesin is removed from chromosome arms by the phosphorylation-dependent prophase pathway. Centromeric cohesin is protected by shugoshin 1 and protein phosphatase 2A (Sgo1-PP2A) and opened only in anaphase by separase-dependent cleavage of Scc1 (refs 4-6). Following chromosome segregation, centrioles loosen their tight orthogonal arrangement, which licenses later centrosome duplication in S phase. Although a role of separase in centriole disengagement has been reported, the molecular details of this process remain enigmatic. Here, we identify cohesin as a centriole-engagement factor. Both premature sister-chromatid separation and centriole disengagement are induced by ectopic activation of separase or depletion of Sgo1. These unscheduled events are suppressed by expression of non-cleavable Scc1 or inhibition of the prophase pathway. When endogenous Scc1 is replaced by artificially cleavable Scc1, the corresponding site-specific protease triggers centriole disengagement. Separation of centrioles can alternatively be induced by ectopic cleavage of an engineered Smc3. Thus, the chromosome and centrosome cycles exhibit extensive parallels and are coordinated with each other by dual use of the cohesin ring complex.