Reward-based eating drives are putative mechanisms of uncontrolled eating implicated in obesity and disordered eating (e.g., binge eating). Uncovering the genetic and environmental contributions to reward-related eating, and their genetic correlation with BMI, could shed light on key mechanisms underlying eating and weight-related disorders. We conducted a classical twin study to examine how much variance in uncontrolled eating phenotypes and body mass index (BMI) was explained by genetic factors, and the extent that these phenotypes shared common genetic factors. 353 monozygotic twins and 128 dizygotic twins completed the Reward-based Eating Drive 13 scale, which measures three distinct uncontrolled eating phenotypes (loss of control over eating, preoccupation with thoughts about food, and lack of satiety), and a demographic questionnaire which included height and weight for BMI calculation. We estimated additive genetic (A), common environmental (C), and unique environmental (E) factors for each phenotype, as well as their genetic correlations, with a multivariate ACE model. A common pathway model also estimated whether genetic variance in the uncontrolled eating phenotypes was better explained by a common latent uncontrolled eating factor. There were moderate genetic correlations between uncontrolled eating phenotypes and BMI (.26-.41). Variance from the uncontrolled eating phenotypes was also best explained by a common latent uncontrolled eating factor that was explained by additive genetic factors (52%). These results suggest that uncontrolled eating phenotypes are heritable traits that also share genetic variance with BMI. This has implications for understanding the cognitive mechanisms that underpin obesity and disordered eating. Our study clarifies the degree to which uncontrolled eating phenotypes and BMI are influenced by shared genetics and shows that vulnerability to uncontrolled eating traits is impacted by common genetic factors.