The mitotic checkpoint, also known as the spindle assembly checkpoint, delays anaphase onset until all chromosomes have reached bipolar tension on the mitotic spindle [1–3]. Once this is achieved, the protease separase is activated to cleave the chromosomal cohesin complex, thereby triggering anaphase. Cohesin cleavage releases tension between sister chromatids, but why the mitotic checkpoint now remains silent is poorly understood. Here, using budding yeast as a model, we show that loss of sister chromatid cohesion at anaphase onset would engage the mitotic checkpoint if this was not prevented by concomitant separase-dependent activation of the Cdc14 phosphatase. Cdc14, in turn, inactivates the mitotic checkpoint by dephosphorylating Sli15INCENP, a subunit of the conserved Aurora B kinase complex that forms part of the proposed chromosomal tension sensor. Dephosphorylation-dependent relocation of Sli15INCENP from centromeres to the central spindle during anaphase is seen in organisms from yeast to human [4–8]. Our results suggest that Sli15INCENP dephosphorylation is part of an evolutionarily conserved mechanism that prevents the mitotic checkpoint from reengaging when tension between sister chromatids is lost at anaphase onset.