The Dark Energy Survey (DES) is currently undertaking an observational program 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 DES will obtain pre-discovery images of the regions surrounding an estimated 100 gamma-ray bursts (GRBs) over five years. Once GRBs 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 GRB activity, collates useful 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 GRBs, as well as for identifying key characteristics (e.g., photometric redshifts) of potential GRB host galaxies. We provide the functional details of the DESAlert software as it presently operates, as well as the data products that it produces, and we show sample results from the application of DESAlert to several previously-detected GRBs.