Vanadium dioxide is a strongly correlated material(1-4) that undergoes a metal-insulator transition(5) from a high-temperature, rutile metal to a monoclinic insulating state at 67 degrees C. In recent years, experiments on single-crystal vanadium-dioxide nanowires grown by physical vapour deposition6 have shed light on the crucial role of strain in the structural and electronic phase diagram of this material(7-10), including evidence for a new M2 phase(11,12), but the detailed physics of this material is still not fully understood. The transition temperature can be reduced by doping with tungsten(8,13), but this process is not reversible. Here, we show that the metal-insulator transition in nanoscale beams of vanadium dioxide can be strongly modified by doping with atomic hydrogen(14) using the catalytic spillover method(15). We also show that this process is completely reversible, and that the metal-insulator transition eventually vanishes when the doping exceeds a threshold value. Raman and conventional optical microscopy, electron diffraction and transmission electron microscopy provide evidence that the structure of the metallic post-hydrogenation state is similar to that of the rutile state. First-principles electronic structure calculations confirm that a distorted rutile structure is energetically favoured following hydrogenation, and also that such doping favours metallicity from both the Mott and Peierls perspectives. We anticipate that hydrogen doping will be a powerful tool for examining the metal-insulator transition and for engineering the properties of vanadium dioxide.