We present the lens mass model of the quadruply-imaged gravitationally lensed quasar WFI2033 - 4723, and perform a blind cosmographical analysis based on this system. Our analysis combines (1) time-delay measurements from 14 yr of data obtained by the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL) collaboration, (2) high-resolution Hubble Space Telescope imaging, (3) a measurement of the velocity dispersion of the lens galaxy based on ESO-MUSE data, and (4) multi-band, wide-field imaging and spectroscopy characterizing the lens environment. We account for all known sources of systematics, including the influence of nearby perturbers and complex line-of-sight structure, as well as the parametrization of the light and mass profiles of the lensing galaxy. After unblinding, we determine the effective time-delay distance to be 4784(-248)(+399) Mpc, an average precision of 6.6 per cent. This translates to a Hubble constant H-0 = 71.6(-4.9)(+3.8) km s(-1) Mpc(-1), assuming a flat Lambda CDM cosmology with a uniform prior on Omega(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 six strongly lensed systems are presented in a companion paper (H0LiCOW XIII).