A search for heavy resonances with masses above 1 TeVTeV, decaying to final states containing a vector boson and a Higgs boson, is presented. The search considers hadronic decays of the vector boson, and Higgs boson decays to b quarks. The decay products are highly boosted, and each collimated pair of quarks is reconstructed as a single, massive jet. The analysis is performed using a data sample collected in 2016 by the CMS experiment at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeVTeV, corresponding to an integrated luminosity of 35.9 fb−1fb−1. The data are consistent with the background expectation and are used to place limits on the parameters of a theoretical model with a heavy vector triplet. In the benchmark scenario with mass-degenerate W′W′ and Z′Z′ bosons decaying predominantly to pairs of standard model bosons, for the first time heavy resonances for masses as high as 3.3 TeVTeV are excluded at 95% confidence level, setting the most stringent constraints to date on such states decaying into a vector boson and a Higgs boson.