The replication factors Cdt1 and Cdc6 are essential for origin licensing, a prerequisite for DNA replication initiation. Mechanisms to ensure that metazoan origins initiate once per cell cycle include degradation of Cdt1 during S phase and inhibition of Cdt1 by the geminin protein. Geminin depletion or overexpression of Cdt1 or Cdc6 in human cells causes rereplication, a form of endogenous DNA damage. Rereplication induced by these manipulations is however uneven and incomplete, suggesting that one or more mechanisms restrain rereplication once it begins. We find that both Cdt1 and Cdc6 are degraded in geminin-depleted cells. We further show that Cdt1 degradation in cells that have rereplicated requires the PCNA binding site of Cdt1 and the Cul4DDB1 ubiquitin ligase, and Cdt1 can induce its own degradation when overproduced. Cdc6 degradation in geminin-depleted cells requires Huwe1, the ubiquitin ligase that regulates Cdc6 after DNA damage. Moreover, perturbations that specifically disrupt Cdt1 and Cdc6 degradation in response to DNA damage exacerbate rereplication when combined with geminin depletion, and this enhanced rereplication occurs in both human cells and in Drosophila melanogaster cells. We conclude that rereplication-associated DNA damage triggers Cdt1 and Cdc6 ubiquitination and destruction, and propose that this pathway represents an evolutionarily conserved mechanism that minimizes the extent of rereplication.