Atrial tachy-arrhytmias, such as atrial fibrillation (AF), are characterised by irregular electrical activity in the atria, generally associated with erratic excitation underlain by re-entrant scroll waves, fibrillatory conduction of multiple wavelets or rapid focal activity. Epidemiological studies have shown an increase in AF prevalence in the developed world associated with an ageing society, highlighting the need for effective treatment options. Catheter ablation therapy, commonly used in the treatment of AF, requires spatial information on atrial electrical excitation. The standard 12-lead electrocardiogram (ECG) provides a method for non-invasive identification of the presence of arrhythmia, due to irregularity in the ECG signal associated with atrial activation compared to sinus rhythm, but has limitations in providing specific spatial information. There is therefore a pressing need to develop novel methods to identify and locate the origin of arrhythmic excitation. Invasive methods provide direct information on atrial activity, but may induce clinical complications. Non-invasive methods avoid such complications, but their development presents a greater challenge due to the non-direct nature of monitoring. Algorithms based on the ECG signals in multiple leads (e.g. a 64-lead vest) may provide a viable approach. In this study, we used a biophysically detailed model of the human atria and torso to investigate the correlation between the morphology of the ECG signals from a 64-lead vest and the location of the origin of rapid atrial excitation arising from rapid focal activity and/or re-entrant scroll waves. A focus-location algorithm was then constructed from this correlation. The algorithm had success rates of 93% and 76% for correctly identifying the origin of focal and re-entrant excitation with a spatial resolution of 40 mm, respectively. The general approach allows its application to any multi-lead ECG system. This represents a significant extension to our previously developed algorithms to predict the AF origins in association with focal activities.