Friedreich (FRDA) and spinocerebellar ataxias (SCAs) are slowly progressing and highly debilitating diseases. The fractal dimension (FD) is a promising quantitative index of structural brain complexity derived from magnetic resonance imaging (MRI) data, with the potential to provide further insights into the changes underlying abnormal brain development and aging in these diseases. We collected brain MRI, genetic and clinical data of 845 patients with inherited cerebellar disorders and 1125 healthy controls (HC) from 16 clinical centers through the ENIGMA-Ataxia international consortium. We developed a computational pipeline and strict quality control for T1-weighted MRI image processing. Cerebral and cerebellar gray matter (GM) and white matter (WM) segmentation, volume, cortical thickness, and FD measures were extracted. After feature harmonization using Combat algorithm, we adopted an explainable artificial intelligence based on XGBoost and SHAP explanations to evaluate the FD as a novel imaging biomarker in identifying, at a single-patient level, FRDA or SCAs patients vs. HC. Specifically, we conducted a study in FRDA (271 patients vs. 603 age- and sex-matched HC), SCA1 (94 patients vs. 578 HC), SCA2 (58 patients vs. 208 HC), SCA3 (161 patients vs. 476 HC), and SCA6 (30 patients vs. 85 HC). In all diseases, the area under the receiver operating curve (ROC) in classifying disease vs. HC group was excellent (range 0.89-0.96). More importantly, the FD of the cerebellar WM or GM was the top-ranking classifying feature for all diseases, but SCA1 in which it was the second feature. Moreover, several FD abnormalities significantly correlated with genetic and clinical features (adjusted p<0.05). Our study results indicate that FD may represent a consistent feature in characterizing inherited ataxias that can complement standard imaging and provides leading innovation and cutting-edge computational approaches to better understand disease pathophysiology.