The Next Generation Virgo Cluster Survey (NGVS) was designed to provide a deep census of baryonic structures in the Virgo cluster. The survey covers the 104 deg2 area from the core of Virgo out to one virial radius, in the u∗griz bandpasses, to a point-source depth of g ∼ 25.9 mag (10σ) and a single pixel surface brightness limit of μ g ∼ 29 mag arcsec-2 (2σ above the sky). Here we present the final catalog of 404 Virgo galaxies located within a 3.71 deg2 (0.3 Mpc2) region centered on M87, Virgo's dominant galaxy. Of these, 154 were previously uncataloged and span the range 17.8 mag < g < 23.7 mag (-13.4 mag < M g < -7.4 mag at the 16.5 Mpc distance of Virgo). Extensive simulations show that the NGVS catalog is complete down to g = 18.6 mag (M g = -12.5 mag, corresponding to a stellar mass ℳ ∼ 1.6 × 107 ℳ for an old stellar population), and 50% complete at g = 22.0 mag (M g = -9.1 mag, ℳ ∼ 6.2 × 105 M⊙). The NGVS 50% completeness limit is 3 mag deeper than that of the Virgo Cluster Catalog (VCC), which has served as Virgo's reference standard for over a quarter century, and 2 mag deeper than the VCC detection limit. We discuss the procedure adopted for the identification of objects and the criteria used to assess cluster membership. For each of the 404 galaxies in the NGVS Virgo Cluster core catalog, we present photometric and structural parameters based on a nonparametric curve-of-growth and isophotal analysis, as well as parametric (Sérsic, double-Sérsic, and/or core-Sérsic) fits to the one-dimensional surface brightness profiles and two-dimensional light distributions.