  We present the full Hubble diagram of photometrically-classified Type Ia
supernovae (SNe Ia) from the Dark Energy Survey supernova program (DES-SN).
DES-SN discovered more than 20,000 SN candidates and obtained spectroscopic
redshifts of 7,000 host galaxies. Based on the light-curve quality, we select
1635 photometrically-identified SNe Ia with spectroscopic redshift 0.10$< z
<$1.13, which is the largest sample of supernovae from any single survey and
increases the number of known $z>0.5$ supernovae by a factor of five. In a
companion paper, we present cosmological results of the DES-SN sample combined
with 194 spectroscopically-classified SNe Ia at low redshift as an anchor for
cosmological fits. Here we present extensive modeling of this combined sample
and validate the entire analysis pipeline used to derive distances. We show
that the statistical and systematic uncertainties on cosmological parameters
are $\sigma_{\Omega_M,{\rm stat+sys}}^{\Lambda{\rm CDM}}=$0.017 in a flat
$\Lambda$CDM model, and $(\sigma_{\Omega_M},\sigma_w)_{\rm stat+sys}^{w{\rm
CDM}}=$(0.082, 0.152) in a flat $w$CDM model. Combining the DES SN data with
the highly complementary CMB measurements by Planck Collaboration (2020)
reduces uncertainties on cosmological parameters by a factor of 4. In all
cases, statistical uncertainties dominate over systematics. We show that
uncertainties due to photometric classification make up less than 10% of the
total systematic uncertainty budget. This result sets the stage for the next
generation of SN cosmology surveys such as the Vera C. Rubin Observatory's
Legacy Survey of Space and Time.
