Deep Brain Stimulation (DBS) is an effective therapy for patients disabling motor symptoms from Parkinson's disease, essential tremor, and other motor disorders. Precise, individualized placement of DBS electrodes is a key contributor to clinical outcomes following surgery. Electroencephalography (EEG) is widely used to identify the sources of intracerebral signals from the potential on the scalp. EEG is portable, non-invasive, low-cost, and it could be easily integrated into the intraoperative or ambulatory environment for localization of either the DBS electrode or evoked potentials triggered by stimulation itself. In this work, we studied with numerical simulations the principle of extracting the DBS electrical pulse from the patient's EEG - which normally constitutes an artifact - and localizing the source of the artifact (i.e., the DBS electrodes) using EEG localization methods. A high-resolution electromagnetic head model was used to simulate the EEG potential at the scalp generated by the DBS pulse artifact. The potential distribution on the scalp was then sampled at the 256 electrode locations of a high-density EEG Net. The electric potential was modeled by a dipole source created by a given pair of active DBS electrodes. The dynamic Statistical Parametric Maps (dSPM) algorithm was used to solve the EEG inverse problem, and it allowed localization of the position of the stimulus dipole in three DBS electrode bipolar configurations with a maximum error of 1.5 cm. To assess the accuracy of the computational model, the results of the simulation were compared with the electric artifact amplitudes over 16 EEG electrodes measured in five patients. EEG artifacts measured in patients confirmed that simulated data are commensurate to patients' data (0 ± 6.6 μV). While we acknowledge that further work is necessary to achieve a higher accuracy needed for surgical navigation, the results presented in this study are proposed as the first step toward a validated computational framework that could be used for non-invasive localization not only of the DBS system but also brain rhythms triggered by stimulation at both proximal and distal sites in the human central nervous system.