Hydrogen spillover (H-spillover) is the surface migration of activated hydrogen atoms from a metallic particle on which they are generated onto a support. The phenomenon has been widely studied because of its implication in hydrogen storage and in catalytic reactions involving hydrogen. Its existence on carbon materials is well established, but questions remain regarding its mechanism and the involvement of surface oxygen groups. In this study, we combined experimental work with chemical modeling to study the mechanisms of H-spillover on a representative system, including a carbon material presenting basal and prismatic surfaces: oxidized carbon nanotubes doped with Pd. The experimental results, supported by those of modeling, show that the surface carboxylic acid groups are the key species, allowing the spillover of hydrogen on carbon materials to take place. The carboxylic groups can also work in combination with phenol groups to facilitate H-spillover. If the concentration of these groups is too low, then the H-spillover does not operate, except in the case of the addition of water, which serves as a shuttle for the protons. This study leads to a deeper understanding of the long-debated issue of H-spillover on carbon materials and provides insight into designing systems with enhanced properties.