  We present a catalog of 316 trans-Neptunian bodies detected by the Dark
Energy Survey (DES). These objects include 245 discoveries by DES (139 not
previously published) detected in $\approx 60,000$ exposures from the first
four seasons of the survey ("Y4" data). The survey covers a contiguous 5000
deg$^2$ of the southern sky in the $grizY$ optical/NIR filter set, with a
typical TNO in this part of the sky being targeted by $25-30$ Y4 exposures. We
describe the processes for detection of transient sources and the linkage into
TNO orbits, which are made challenging by the absence of the few-hour repeat
observations employed by TNO-optimized surveys. We also describe the procedures
for determining detection efficiencies vs. magnitude and estimating rates of
false-positive linkages. This work presents all TNOs which were detected on
$\ge 6$ unique nights in the Y4 data and pass a "sub-threshold confirmation"
test wherein we demand the the object be detectable in a stack of the
individual images in which the orbit indicates an object should be present, but
was not detected. This eliminates false positives and yields TNO detections
complete to $r\lesssim 23.3$ mag with virtually no dependence on orbital
properties for bound TNOs at distance $30\,{\rm AU}<d<2500\,{\rm AU}.$ The
final DES TNO catalog is expected to yield $>0.3$ mag more depth, and arcs of
$>4$ years for nearly all detections.
