  We present a catalog of 23,790 extended low-surface-brightness galaxies
(LSBGs) identified in $\sim 5000 \deg^2$ from the first three years of imaging
data from the Dark Energy Survey (DES). Based on a single-component S\'ersic
model fit, we define extended LSBGs as galaxies with $g$-band effective radii
$R_{eff}(g) > 2.5''$ and mean surface brightness $\bar{\mu}_{eff}(g) > 24.2
\,mag \.arcsec^{-2}$. We find that the distribution of LSBGs is strongly
bimodal in $(g-r)$ vs.\ $(g-i$) color space. We divide our sample into red
($g-i \geq 0.60$) 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 $\sim 33\%$ of our LSBG sample, and $\sim
30\%$ of these are located within 1 deg of low-redshift galaxy groups and
clusters (compared to $\sim 8\%$ 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 ultra-diffuse
galaxies, defined as LSBGs with projected physical effective radii $R_{eff} >
1.5 \,kpc$ and central surface brighthness $\mu_0(g) > 24.0\, mag
\,arcsec^{-2}$. The wide-area sample of LSBGs in DES can be used to test the
role of environment on models of LSBG formation and evolution.
