In GaAsyN(1-y), the presence of a few percent of N induces a large reduction of the GaAs band gap that vanishes upon hydrogenation. In the present Letter, the energetics of N-H complexes and their effects on the band structure of the GaAs0.97N0.03 alloy have been investigated by first-principles density functional methods. We find that monohydrogen N-H+ and dihydrogen N-H* 2 complexes are formed depending on doping. Moreover, only N-H* 2 complexes account for the neutralization of nitrogen effects. A model is proposed that clarifies the passivation mechanism of nitrogen by H.