We study the vacuum stability and unitarity conditions for a 125 GeV Standard Model (SM)-like Higgs boson mass in the type-II seesaw model. We find that, as long as the seesaw scale is introduced below the SM vacuum instability bound, there exists a large parameter space predicting a 125 GeV Higgs mass, irrespective of the exact value of the seesaw scale, satisfying both stability and unitarity conditions up to the Planck scale. We also study the model predictions for the Higgs partial decay widths in the diphoton and Z+photon channels with respect to their SM expectations and find that the decay rates for these two processes are anti- correlated. We further show that for any given enhancement in the Higgs-to-diphoton rate over its SM expectation, there exists an upper bound on the type-II seesaw scale, and hence, on the masses of the associated doubly- and singly-charged Higgs bosons in the allowed parameter space. For instance, if more than 10% enhancement persists in the Higgs-to-diphoton channel, the upper limit on the type-II seesaw scale is about 450 GeV which is completely within the reach of the 14 TeV LHC. We believe this to be an encouraging result for the experimental searches of the singly- and doubly-charged Higgs bosons which, in combination with improved sensitivity in the Higgs-to-diphoton and Higgs-to-Z+photon channels, could probe the entire allowed parameter space of the minimal type-II seesaw model, and establish/eliminate it as a single viable extension of the SM.