The Dark Energy Survey is undertaking an observational programme imaging 1/4 of the southern hemisphere sky with unprecedented photometric accuracy. In the process of observing millions of faint stars and galaxies to constrain the parameters of the dark energy equation of state, the Dark Energy Survey will obtain pre-discovery images of the regions surrounding an estimated 100 gamma-ray bursts over 5 yr. Once gamma-ray bursts are detected by, e.g., the Swift satellite, the DES data will be extremely useful for follow-up observations by the transient astronomy community. We describe a recently-commissioned suite of software that listens continuously for automated notices of gamma-ray burst activity, collates information from archival DES data, and disseminates relevant data products back to the community in near-real-time. Of particular importance are the opportunities that non-public DES data provide for relative photometry of the optical counterparts of gamma-ray bursts, as well as for identifying key characteristics (e.g., photometric redshifts) of potential gamma-ray burst host galaxies. We provide the functional details of the DESAlert software, and its data products, and we show sample results from the application of DESAlert to numerous previously detected gamma-ray bursts, including the possible identification of several heretofore unknown gamma-ray burst hosts.