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We present a new measurement of the Hubble Constant H0 and other cosmologicalparameters based on the joint analysis of three multiply-imaged quasar systemswith measured gravitational time delays. First, we measure the time delay ofHE0435-1223 from 13-year light curves obtained as part of the COSMOGRAILproject. Companion papers detail the modeling of the main deflectors and lineof sight effects, and how these data are combined to determine the time-delaydistance of HE 0435-1223. Crucially, the measurements are carried out blindlywith respect to cosmological parameters in order to avoid confirmation bias. Wethen combine the time-delay distance of HE0435-1223 with previous measurementsfrom systems B1608+656 and RXJ1131-1231 to create a Time Delay Strong Lensingprobe (TDSL). In flat $\Lambda$CDM with free matter and energy density, we find$H_0$ = 71.9 +2.4 -3.0 km/s/Mpc and $\Omega_{\Lambda}$ = 0.62 +0.24 -0.35 .This measurement is completely independent of, and in agreement with, the localdistance ladder measurements of H0. We explore more general cosmological modelscombining TDSL with other probes, illustrating its power to break degeneraciesinherent to other methods. The TDSL and Planck joint constraints are $H_0$ =69.2 +1.4 -2.2 km/s/Mpc, $\Omega_{\Lambda}$ = 0.70 +0.01 -0.01 and $\Omega_k$ =0.003 +0.004 -0.006 in open $\Lambda$CDM and $H_0$ = 79.0 +4.4 -4.2 km/s/Mpc,$\Omega_{de}$ = 0.77 +0.02 -0.03 and $w$ = -1.38 +0.14 -0.16 in flat $w$CDM.Combined with Planck and Baryon Acoustic Oscillation data, when relaxing theconstraints on the numbers of relativistic species we find $N_{eff}$ = 3.34+0.21 -0.21 and when relaxing the total mass of neutrinos we find 0.182 eV. Inan open $w$CDM in combination with Planck and CMB lensing we find $H_0$ = 77.9+5.0 -4.2 km/s/Mpc, $\Omega_{de}$ = 0.77 +0.03 -0.03, $\Omega_k$ = -0.003+0.004 -0.004 and $w$ = -1.37 +0.18 -0.23.

H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: $H_0$ to 3.8% precision from strong lensing in a flat $\Lambda$CDM model