Psychiatry is undergoing a paradigm shift from the acceptance of distinct diagnoses to a representation of psychiatric illness that crosses diagnostic boundaries. How this transition is supported by a shared neurobiology remains largely unknown. In this study, we first identify single nucleotide polymorphisms (SNPs) associated with psychiatric disorders based on 136 genome-wide association studies. We then conduct a joint analysis of these SNPs and brain structural connectomes in 678 healthy children in the PING study. We discovered a strong, robust, and transdiagnostic mode of genome-connectome covariation which is positively and specifically correlated with genetic risk for psychiatric illness at the level of individual SNPs. Similarly, this mode is also significantly positively correlated with polygenic risk scores for schizophrenia, alcohol use disorder, major depressive disorder, a combined bipolar disorder-schizophrenia phenotype, and a broader cross-disorder phenotype, and significantly negatively correlated with a polygenic risk score for educational attainment. The resulting "vulnerability network" is shown to mediate the influence of genetic risks onto behaviors related to psychiatric vulnerability (e.g., marijuana, alcohol, and caffeine misuse, perceived stress, and impulsive behavior). Its anatomy overlaps with the default-mode network, with a network of cognitive control, and with the occipital cortex. These findings suggest that the brain vulnerability network represents an endophenotype funneling genetic risks for various psychiatric illnesses through a common neurobiological root. It may form part of the neural underpinning of the well-recognized but poorly explained overlap and comorbidity between psychiatric disorders.