Depression and anxiety are highly comorbid due to shared genetic risk factors, but less is known about whether burnout shares these risk factors. We aimed to examine whether the covariation between major depressive disorder (MDD), generalized anxiety disorder (GAD), and burnout is explained by common genetic and/or environmental factors. This cross-sectional study included 25,378 Swedish twins responding to a survey in 2005–2006. Structural equation models were used to analyze whether the trait variances and covariances were due to additive genetics, non-additive genetics, shared environment, and unique environment. Univariate analyses tested sex limitation models and multivariate analysis tested Cholesky, independent pathway, and common pathway models. The phenotypic correlations were 0.71 (0.69–0.74) between MDD and GAD, 0.58 (0.56–0.60) between MDD and burnout, and 0.53 (0.50–0.56) between GAD and burnout. Heritabilities were 45% for MDD, 49% for GAD, and 38% for burnout; no statistically significant sex differences were found. A common pathway model was chosen as the final model. The common factor was influenced by genetics (58%) and unique environment (42%), and explained 77% of the variation in MDD, 69% in GAD, and 44% in burnout. GAD and burnout had additive genetic factors unique to the phenotypes (11% each), while MDD did not. Unique environment explained 23% of the variability in MDD, 20% in GAD, and 45% in burnout. In conclusion, the covariation was explained by an underlying common factor, largely influenced by genetics. Burnout was to a large degree influenced by unique environmental factors not shared with MDD and GAD.