Despite the frequent use of noble gas ion irradiation of graphene, the atomistic scale details, including the effects of dose, energy, and ion bombardment species on defect formation, and the associated dynamic processes involved in the irradiations and subsequent relaxation, have not yet been thoroughly studied. Here, we simulated the irradiation of graphene with noble gas ions, and the subsequent effects of annealing. Lattice defects, including nanopores, were generated after the annealing of the irradiated graphene, which was the result of structural relaxation that allowed the vacancy-type defects to coalesce into a larger defect. Larger nanopores were generated by irradiation with a series of heavier noble gas ions, due to a larger collision cross-section that led to more detrimental effects in the graphene, and by a higher ion dose that increased the chance of displacing the carbon atoms from graphene. Overall trends in the evolution of defects with respect to a dose, as well as the defect characteristics, were in good agreement with experimental results. Additionally, the statistics in the defect types generated by different irradiating ions suggested that the most frequently observed defect types were Stone-Thrower-Wales (STW) defects for He+ irradiation and mono-vacancy (MV) defects for all other ion irradiations.