Eating disorders, including anorexia nervosa, bulimia nervosa and binge eating disorder, are psychiatric conditions associated with high mortality rates, particularly due to suicide. Although eating disorders are strongly associated with suicidal ideation, attempts, and fatalities, the precise relationship between these conditions remains poorly understood. While substantial genetic influences have been identified for both eating disorders and suicidality, the shared genetics contributing to their co-occurrence remain unclear. In this study, we utilized a multivariate approach to examine the shared genetic architecture of eating disorder symptoms, suicidal thoughts and behaviors in ~20,000 participants from the COVID-19 Psychiatry and Neurological Genetics (COPING) study. We applied individual-level structural equation modeling to explore the factor structure underlying eating disorder symptoms and suicidal ideation, followed by genetic correlation analyses. We modeled the general factor of susceptibility to eating disorders and suicidal ideation that was as strongly genetically influenced as both conditions, with mean SNP heritability of 9%. Importantly, despite the frequent co-occurrence of eating disorders with other psychiatric conditions, our findings highlight the specificity of the relationship between eating disorders and suicidality, independent of other co-occurring psychopathology, such as depression and anxiety. This specificity highlights the need for targeted approaches in understanding the shared susceptibility factors.