We present the first set of trans-Neptunian objects (TNOs) observed on multiple nights in data taken from the DECam Ecliptic Exploration Project. Of these 110 TNOs, 105 do not coincide with previously known TNOs and appear to be new discoveries. Each individual detection for our objects resulted from a digital tracking search at TNO rates of motion, using two-to-four-hour exposure sets, and the detections were subsequently linked across multiple observing seasons. This procedure allows us to find objects with magnitudes mVR~26. The object discovery processing also included a comprehensive population of objects injected into the images, with a recovery and linking rate of at least 94%. The final orbits were obtained using a specialized orbit-fitting procedure that accounts for the positional errors derived from the digital tracking procedure. Our results include robust orbits and magnitudes for classical TNOs with absolute magnitudes H~10, as well as a dynamically detached object found at 76au (semimajor axis a~77au). We find a disagreement between our population of classical TNOs and the CFEPS-L7 three-component model for the Kuiper Belt.