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We investigate the electronic and optical properties of hydrogenated H_xVO₂. We find doping-dependent metal-insulator transitions as increasing hydrogen content from the optical conductivity measured by spectroscopic ellipsometry, showing a gap opening with a structural transition forming V-V dimer as increasing the H doping. The insulating phase is investigated using density functional and dynamical mean-field theory. We identify the orbital-ordered paramagnetic insulating phase as the ground state of HVO₂ in which both the dimer-induced bonding-antibonding splitting and the orbital ordering stabilized by electron correlations play an important role in the metal-insulator transition. We compare the calculated optical conductivity of the metallic and insulating phases with experimental data and discuss the increase in the charge transfer energy with high hydrogen content.