Abnormal numerical and structural chromosome content is frequently found in human cancer. To test the role of aneuploidy in tumor initiation and progression, we generated mice with random aneuploidies by transient induction of polo-like kinase 4 (Plk4), a master regulator of centrosome number. Short-term chromosome instability (CIN) from transient Plk4 induction resulted in formation of aggressive T-cell lymphomas in mice with heterozygous inactivation of one allele and accelerated tumor development in the absence of p53. Transient CIN increased the frequency of lymphoma-initiating cells with a specific karyotype profile, including trisomy of chromosomes 4, 5, 14, and 15 occurring early in tumorigenesis. Tumor development in mice with chronic CIN induced by an independent mechanism (through inactivation of the spindle assembly checkpoint) gradually trended toward a similar karyotypic profile, as determined by single-cell whole-genome DNA sequencing. Overall, we show how transient CIN generates cells with random aneuploidies from which ones that acquire a karyotype with specific chromosome gains are sufficient to drive cancer formation, and that distinct CIN mechanisms can lead to similar karyotypic cancer-causing outcomes.