Electrooculography (EOG) is the measurement of eye movements using surface electrodes adhered around the eye. EOG systems can be designed to have an unobtrusive form-factor that is ideal for eye tracking in free-living over long durations, but the relationship between voltage and gaze direction requires frequent re-calibration as the skin-electrode impedance and retinal adaptation vary over time. Here we propose a method for automatically calibrating the EOG-gaze relationship by fusing EOG signals with gyroscopic measurements of head movement whenever the vestibulo-ocular reflex (VOR) is active. The fusion is executed as recursive inference on a hidden Markov model that accounts for all rotational degrees-of-freedom and uncertainties simultaneously. This enables continual calibration using natural eye and head movements while minimizing the impact of sensor noise. No external devices like monitors or cameras are needed. On average, our method's gaze estimates deviate by 3.54° from those of an industry-standard desktop video-based eye tracker. Such discrepancy is on par with the latest mobile video eye trackers. Future work is focused on automatically detecting moments of VOR in free-living.