Brain atlas is an important tool in the diagnosis and treatment of neurological disorders. However, due to large variations in the organizational principles of individual brains, many challenges remain in clinical applications. Brain atlas individualization network (BAI-Net) is an algorithm that subdivides individual cerebral cortex into segregated areas using brain morphology and connectomes. The presented method integrates group priors derived from a population atlas, adjusts areal probabilities using the context of connectivity fingerprints derived from the fiber-tract embedding of tractography, and provides reliable and explainable individualized brain areas across multiple sessions and scanners. We demonstrate that BAI-Net outperforms the conventional iterative clustering approach by capturing significantly heritable topographic variations in individualized cartographies. The topographic variability of BAI-Net cartographies has shown strong associations with individual variability in brain morphology, connectivity as well as higher relationship on individual cognitive behaviors and genetics. This study provides an explainable framework for individualized brain cartography that may be useful in the precise localization of neuromodulation and treatments on individual brains.