  We present a catalog of physical properties for galaxies hosting active
galactic nuclei (AGN) detected by the Wide-field Infrared Survey Explorer
(WISE). By fitting broadband spectral energy distributions of sources in the
WISE AGN Catalog (Assef et al. 2018) with empirical galaxy and AGN templates,
we derive photometric redshifts, AGN bolometric luminosities, measures of AGN
obscuration, host galaxy stellar masses, and host galaxy star formation rates
(SFRs) for 695,273 WISE AGN. The wide-area nature of this catalog significantly
augments the known number of obscured AGN out to redshifts of z~3 and will be
useful for studies focused on AGN or their host galaxy physical properties. We
first show that the most likely non-AGN contaminants are galaxies at redshifts
of z=0.2-0.3, with relatively blue W1-W2 colors, and with high specific SFRs
for which the dust continuum emission is elevated in the W2 filter. Toward
increasingly lower redshifts, WISE AGN host galaxies have systematically lower
specific SFRs, relative to those of normal star forming galaxies, likely due to
decreased cold gas fractions and the time delay between global star formation
and AGN triggering. Finally, WISE AGN obscuration is not strongly correlated
with AGN bolometric luminosity but shows a significant negative correlation
with Eddington ratio. This result is consistent with a version of the `receding
torus' model in which the obscuring material is located within the supermassive
black hole gravitational sphere of influence and the dust inner radius
increases due to radiation pressure.
