The left atrium (LA) can change in size and shape due to atrial fibrillation (AF)-induced remodeling. These alterations can be linked to poorer outcomes of AF ablation. In this study, we propose a novel comprehensive computational analysis of LA anatomy to identify what features of LA shape can optimally predict post-ablation AF recurrence. To this end, we construct smooth 3D geometrical models from the segmentation of the LA blood pool captured in pre-procedural MR images. We first apply this methodology to characterize the LA anatomy of 144 AF patients and build a statistical shape model that includes the most salient variations in shape across this cohort. We then perform a discriminant analysis to optimally distinguish between recurrent and non-recurrent patients. From this analysis, we propose a new shape metric called vertical asymmetry, which measures the imbalance of size along the anterior to posterior direction between the superior and inferior left atrial hemispheres. Vertical asymmetry was found, in combination with LA sphericity, to be the best predictor of post-ablation recurrence at both 12 and 24 months (area under the ROC curve: 0.71 and 0.68, respectively) outperforming other shape markers and any of their combinations. We also found that model-derived shape metrics, such as the anterior-posterior radius, were better predictors than equivalent metrics taken directly from MRI or echocardiography, suggesting that the proposed approach leads to a reduction of the impact of data artifacts and noise. This novel methodology contributes to an improved characterization of LA organ remodeling and the reported findings have the potential to improve patient selection and risk stratification for catheter ablations in AF.