We present the ugriz-band Dark Energy Camera (DECam) plus 3.6 and 4.5{mu}m IRAC catalogs for the Spitzer/HETDEX Exploratory Large-Area (SHELA) survey. SHELA covers ~24deg^2^ of the Sloan Digital Sky Survey (SDSS) "Stripe 82" region, with seven bandpasses spanning a wavelength range of 0.35 to 4.5{mu}m. SHELA falls within the footprint of the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX), which will provide spectroscopic redshifts for ~200000 Ly{alpha} emitters at 1.9<z<3.5 and also for ~200000 [OII] emitters at z<0.5. SHELA's deep, wide-area multiwavelength images, combined with HETDEX's spectroscopic information, will facilitate many extragalactic studies, including measuring the evolution of galaxy stellar mass, halo mass, and environment from 1.5<z<3.5. Here we present riz-band-selected ugriz-band DECam catalogs that reach a 5{sigma} depth of ~24.5 AB mag (for point sources with an aperture that encloses 70% of the total flux) and cover 17.5deg^2^ of the overall SHELA field. We validate our DECam catalog by comparison to the DECam Legacy Survey (DECaLS) DR5 and the Dark Energy Survey (DES) DR1. We perform IRAC forced photometry with The Tractor image modeling code to measure 3.6 and 4.5{mu}m fluxes for all objects within our DECam catalog. We demonstrate the utility of our catalog by computing galaxy number counts and estimating photometric redshifts. Our photometric redshifts recover the available <z>=0.33 SDSS spectroscopic redshifts with a 1{sigma} scatter in {Delta}z/(1+z) of 0.04.