The ubiquitination of cell cycle regulatory proteins by the anaphase-promoting complex/cyclosome (APC/C) controls sister chromatid segregation, cytokinesis and the establishment of the G1 phase of the cell cycle. The APC/C is an unusually large multimeric cullin-RING ligase. Its activity is strictly dependent on regulatory coactivator subunits that promote APC/C–substrate interactions and stimulate its catalytic reaction. Because the structures of many APC/C subunits and their organization within the assembly are unknown, the molecular basis for these processes is poorly understood. Here, from a cryo-electron microscopy reconstruction of a human APC/C–coactivator–substrate complex at 7.4 Å resolution, we have determined the complete secondary structural architecture of the complex. With this information we identified protein folds for structurally uncharacterized subunits, and the definitive location of all 20 APC/C subunits within the 1.2 MDa assembly. Comparison with apo APC/C shows that the coactivator promotes a profound allosteric transition involving displacement of the cullin-RING catalytic subunits relative to the degron-recognition module of coactivator and APC10. This transition is accompanied by increased flexibility of the cullin-RING subunits and enhanced affinity for UBCH10–ubiquitin, changes which may contribute to coactivator-mediated stimulation of APC/C E3 ligase activity.