The centrosome organizes the microtubule cytoskeleton and consists of a pair of centrioles surrounded by pericentriolar material. Cells begin the cell cycle with a single centrosome, which duplicates once before mitosis. During duplication, new centrioles grow orthogonally to existing ones and remain engaged (tightly opposed) with those centrioles until late mitosis or early G1 phase, when they become disengaged. The relationship between centriole engagement/disengagement and centriole duplication potential is not understood, and the mechanisms that control these processes are not known. Here we show that centriole disengagement requires the protease separase at anaphase, and that this disengagement licences centriole duplication in the next cell cycle. We describe an in vitro system using Xenopus egg extract and purified centrioles in which both centriole disengagement and centriole growth occur. Centriole disengagement at anaphase is independent of mitotic exit and Cdk2/cyclin E activity, but requires the anaphase-promoting complex and separase. In contrast to disengagement, new centriole growth occurs in interphase, is dependent on Cdk2/cyclin E, and requires previously disengaged centrioles. This suggests that re-duplication of centrioles within a cell cycle is prevented by centriole engagement itself. We propose that the 'once-only' control of centrosome duplication is achieved by temporally separating licensing in anaphase from growth of new centrioles during S phase. The involvement of separase in both centriole disengagement and sister chromatid separation would prevent premature centriole disengagement before anaphase onset, which can lead to multipolar spindles and genomic instability.