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We present the lens mass model of the quadruply-imaged gravitationally lensedquasar WFI2033-4723, and perform a blind cosmographical analysis based on thissystem. Our analysis combines (1) time-delay measurements from 14 years of dataobtained by the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL)collaboration, (2) high-resolution $\textit{Hubble Space Telescope}$ imaging,(3) a measurement of the velocity dispersion of the lens galaxy based onESO-MUSE data, and (4) multi-band, wide-field imaging and spectroscopycharacterizing the lens environment. We account for all known sources ofsystematics, including the influence of nearby perturbers and complexline-of-sight structure, as well as the parametrization of the light and massprofiles of the lensing galaxy. After unblinding, we determine the effectivetime-delay distance to be $4784_{-248}^{+399}~\mathrm{Mpc}$, an averageprecision of $6.6\%$. This translates to a Hubble constant $H_{0} =71.6_{-4.9}^{+3.8}~\mathrm{km~s^{-1}~Mpc^{-1}}$, assuming a flat $\Lambda$CDMcosmology with a uniform prior on $\Omega_\mathrm{m}$ in the range [0.05, 0.5].This work is part of the $H_0$ Lenses in COSMOGRAIL's Wellspring (H0LiCOW)collaboration, and the full time-delay cosmography results from a total of sixstrongly lensed systems are presented in a companion paper (H0LiCOW XIII).

H0LiCOW XII. Lens mass model of WFI2033-4723 and blind measurement of its time-delay distance and $H_0$