We present a catalog of 23790 extended low-surface-brightness galaxies (LSBGs) identified in ~5000{deg}^2^ from the first three years of imaging data from the Dark Energy Survey (DES). Based on a single-component Sersic model fit, we define extended LSBGs as galaxies with g-band effective radii R_eff_(g)>2.5" and mean surface brightness {mu}_eff_(g)>24.2mag/arcsec^2^}. We find that the distribution of LSBGs is strongly bimodal in (g-r) versus (g-i) color space. We divide our sample into red (g-i>=0.60) and blue (g-i<0.60) galaxies and study the properties of the two populations. Redder LSBGs are more clustered than their blue counterparts and are correlated with the distribution of nearby (z<0.10) bright galaxies. Red LSBGs constitute ~33% of our LSBG sample, and ~30% of these are located within 1{deg} of low-redshift galaxy groups and clusters (compared to ~8% of the blue LSBGs). For nine of the most prominent galaxy groups and clusters, we calculate the physical properties of associated LSBGs assuming a redshift derived from the host system. In these systems, we identify 41 objects that can be classified as ultradiffuse galaxies, defined as LSBGs with projected physical effective radii R_eff_>1.5kpc and central surface brightness {mu}_0_(g)>24.0mag/arcsec^2^. The wide-area sample of LSBGs in DES can be used to test the role of environment on models of LSBG formation and evolution.