In early mitosis, the duplicated chromosomes are held together by the ring-shaped cohesin complex1. Separation of chromosomes during anaphase is triggered by separase—a large cysteine endopeptidase that cleaves the cohesin subunit SCC1 (also known as RAD212,3,4). Separase is activated by degradation of its inhibitors, securin5 and cyclin B6, but the molecular mechanisms of separase regulation are not clear. Here we used cryogenic electron microscopy to determine the structures of human separase in complex with either securin or CDK1–cyclin B1–CKS1. In both complexes, separase is inhibited by pseudosubstrate motifs that block substrate binding at the catalytic site and at nearby docking sites. As in Caenorhabditis elegans7 and yeast8, human securin contains its own pseudosubstrate motifs. By contrast, CDK1–cyclin B1 inhibits separase by deploying pseudosubstrate motifs from intrinsically disordered loops in separase itself. One autoinhibitory loop is oriented by CDK1–cyclin B1 to block the catalytic sites of both separase and CDK19,10. Another autoinhibitory loop blocks substrate docking in a cleft adjacent to the separase catalytic site. A third separase loop contains a phosphoserine6 that promotes complex assembly by binding to a conserved phosphate-binding pocket in cyclin B1. Our study reveals the diverse array of mechanisms by which securin and CDK1–cyclin B1 bind and inhibit separase, providing the molecular basis for the robust control of chromosome segregation.