Cyclins B1 and B2 are frequently elevated in human cancers and are associated with tumour aggressiveness and poor clinical outcome; however, whether and how B-type cyclins drive tumorigenesis is unknown. Here we show that cyclin B1 and B2 transgenic mice are highly prone to tumours, including tumour types where B-type cyclins serve as prognosticators. Cyclins B1 and B2 both induce aneuploidy when overexpressed but through distinct mechanisms, with cyclin B1 inhibiting separase activation, leading to anaphase bridges, and cyclin B2 triggering aurora-A-mediated Plk1 hyperactivation, resulting in accelerated centrosome separation and lagging chromosomes. Complementary experiments revealed that cyclin B2 and p53 act antagonistically to control aurora-A-mediated centrosome splitting and accurate chromosome segregation in normal cells. These data demonstrate a causative link between B-type cyclin overexpression and tumour pathophysiology, and uncover previously unknown functions of cyclin B2 and p53 in centrosome separation that may be perturbed in many human cancers.