Cohesin establishes sister-chromatid cohesion from S phase until mitosis or meiosis. To allow chromosome segregation, cohesion has to be dissolved. In vertebrate cells, this process is mediated in part by the protease separase, which destroys a small amount of cohesin, but most cohesin is removed from chromosomes without proteolysis. How this is achieved is poorly understood. Here, we show that the interaction between cohesin and chromatin is controlled by Wapl, a protein implicated in heterochromatin formation and tumorigenesis. Wapl is associated with cohesin throughout the cell cycle, and its depletion blocks cohesin dissociation from chromosomes during the early stages of mitosis and prevents the resolution of sister chromatids until anaphase, which occurs after a delay. Wapl depletion also increases the residence time of cohesin on chromatin in interphase. Our data indicate that Wapl is required to unlock cohesin from a particular state in which it is stably bound to chromatin.