The anaphase-promoting complex (APC/C) orchestrates progression through mitosis by decorating cell-cycle regulators with ubiquitin chains. To nucleate chains, the APC/C links ubiquitin to a lysine in substrates, but to elongate chains it modifies lysine residues in attached ubiquitin moieties. The mechanism enabling the APC/C, and ubiquitin ligases in general, to switch from lysine residues in substrates to specific ones in ubiquitin remains poorly understood. Here, we determine the topology and the mechanism of assembly for the ubiquitin chains mediating functions of the human APC/C. We find that the APC/C triggers substrate degradation by assembling K11-linked ubiquitin chains, the efficient formation of which depends on a surface of ubiquitin, the TEK-box. Strikingly, homologous TEK-boxes are found in APC/C substrates, where they facilitate chain nucleation. We propose that recognition of similar motifs in substrates and ubiquitin enables the APC/C to assemble ubiquitin chains with the specificity and efficiency required for tight cell-cycle control.