The spindle checkpoint delays cell cycle progression until microtubules attach each pair of sister chromosomes to opposite poles of the mitotic spindle. Following sister chromatid separation, however, the checkpoint ignores chromosomes whose kinetochores are attached to only one spindle pole, a state that activates the checkpoint prior to metaphase. We demonstrate that, in budding yeast, mutual inhibition between the anaphase-promoting complex (APC) and Mps1, an essential component of the checkpoint, leads to sustained inactivation of the spindle checkpoint. Mps1 protein abundance decreases in anaphase, and Mps1 is a target of the APC. Furthermore, expression of Mps1 in anaphase, or repression of the APC in anaphase, reactivates the spindle checkpoint. This APC-Mps1 feedback circuit allows cells to irreversibly inactivate the checkpoint during anaphase.