A combined search for high-mass resonances decaying to $WW$, $WZ$, and $ZZ$ final states with jets in boosted topologies is presented. The combination comprises four individual searches in the $\nu\nu qq$, $\ell\nu qq$, $\ell\ell qq$, and $qqqq$ final states, performed in $pp$ collision data corresponding to an integrated luminosity of $3.2~\mathrm{fb}^{-1}$ at $\sqrt{s} = 13~\mathrm{TeV}$ collected by the ATLAS detector at the CERN Large Hadron Collider (LHC). Exclusion limits on the heavy resonance production cross section times branching fraction to dibosons are set at the $95\%$ confidence level for three benchmark signal models. The combined search finds upper exclusion limits on the masses of a scalar singlet, a heavy vector-boson triplet, and a Randall-Sundrum graviton at $2650$, $2600$, and $1100~\mathrm{GeV}$, respectively.