There is a well-established link between sleep disorders and psychological problems such as anxiety and depression. Twin studies and genome-wide association studies (GWAS) have consistently found significant genetic overlap between these traits. However, there is considerable variation among studies. The aims of this meta-analysis were therefore: 1) to estimate the mean genetic correlation between sleep problems and psychological distress; 2) to assess heterogeneity among the included studies; and 3) to search for potential moderators that could contribute to this heterogeneity. To this end, we performed several multivariate meta-analyses. The mean genetic correlations were estimated to be 0.55 (CI: 0.47–0.63) for sleep quality and depression, 0.72 (CI: 0.59–0.85) for insomnia symptoms and depression, 0.42 (CI: 0.30–0.54) for sleep quality and anxiety, and 0.75 (CI: 0.59–0.91) for insomnia symptoms and anxiety. Similar results were obtained when depression and anxiety were collapsed (0.54 [CI: 0.44–0.64] for sleep quality and 0.77 [CI: 0.63–0.91] for insomnia symptoms). Sex did not significantly moderate these associations. Study type (twin studies vs GWAS) and age, however, were significant moderators (p < 0.001). These findings highlight the substantial genetic overlap between psychological distress and sleep problems, which appears to be stronger for insomnia symptoms than for sleep quality.