DNA damage induced by ionizing radiation exposure is enhanced in the presence of oxygen (the “oxygen effect”). Despite its practical importance in radiotherapy, the oxygen effect has largely been excluded from models that predict DNA damage from radiation tracks. A Monte Carlo-based algorithm was developed in MATLAB software to predict DNA damage from physical and chemical tracks through a cell nucleus simulated in Geant4-DNA, taking into account the effects of cellular oxygenation (pO₂) on DNA radical chemistry processes. An initial spatial distribution of DNA base and sugar radicals was determined by spatially clustering direct events (that deposited at least 10.79 eV) and hydroxyl radical (^•OH) interactions. The oxygen effect was modeled by increasing the efficiency with which sugar radicals from direct-type effects were converted to strand breaks from 0.6 to 1, the efficiency with which sugar radicals from the indirect effect were converted to strand breaks from 0.28 to 1 and the efficiency of base-to-sugar radical transfer from ^•OH-mediated base radicals from 0 to 0.03 with increasing pO₂ from 0 to 760 mmHg. The DNA damage induction algorithm was applied to tracks from electrons, protons and alphas with LET values from 0.2 to 150 keV/μm under different pO₂ conditions. The oxygen enhancement ratio for double-strand break induction was 3.0 for low-LET radiation up to approximately 15 keV/μm, after which it gradually decreased to a value of 1.3 at 150 keV/μm. These values were consistent with a range of experimental data published in the literature. The DNA damage yields were verified using experimental data in the literature and results from other theoretical models. The spatial clustering approach developed in this work has low memory requirements and may be suitable for particle tracking simulations with a large number of cells.