Centrosome amplification is a common feature of human tumors, but whether this is a cause or a consequence of cancer remains unclear. Here, we test the consequence of centrosome amplification by creating mice in which centrosome number can be chronically increased in the absence of additional genetic defects. We show that increasing centrosome number elevated tumor initiation in a mouse model of intestinal neoplasia. Most importantly, we demonstrate that supernumerary centrosomes are sufficient to drive aneuploidy and the development of spontaneous tumors in multiple tissues. Tumors arising from centrosome amplification exhibit frequent mitotic errors and possess complex karyotypes, recapitulating a common feature of human cancer. Together, our data support a direct causal relationship among centrosome amplification, genomic instability, and tumor development.