Recent experiments indicate that proton irradiation triggers ferromagnetism in originally nonmagnetic graphite samples while He ion bombardment has a much smaller effect. To understand the origin of irradiation-induced magnetism, we have performed spin-polarized density functional theory calculations of the magnetic properties of the defects which are most likely to appear under irradiation vacancies and vacancy-hydrogen complexes. Both defects are magnetic, but as for the latter we find that H adsorption on one of the vacancy dangling bonds gives rise to a magnetic moment double that of the naked vacancy. We show that for small irradiation doses vacancy-hydrogen complexes result in a macroscopic magnetic signal which agrees well with the experimental values.