Moral Foundations Theory (MFT) predicts that moral behaviour reflects at least five foundational traits, each hypothesised to be heritable. Here, we report two independent twin studies (total n = 2020), using multivariate multi-group common pathway models to test the following three predictions from the MFT: (1) The moral foundations will show significant heritability; (2) The moral foundations will each be genetically distinct and (3) The clustering of moral concerns around individualising and binding domains will show significant heritability. Supporting predictions 1 and 3, Study 1 showed evidence for significant heritability of two broad moral factors corresponding to individualising and binding domains. In Study 2, we added the second dataset, testing replication of the Study 1 model in a joint approach. This further corroborated evidence for heritable influence, showed strong influences on the individualising and binding domains (h2 = 49% and 66%, respectively) and, partially supporting prediction 2, showed foundation-specific, heritable influences on Harm/Care, Fairness/Reciprocity and Purity/Sanctity foundations. A general morality factor was required, also showing substantial genetic effects (40%). These findings indicate that moral foundations have significant genetic bases. These influenced the individual foundations themselves as well as a general concern for the individual, for the group, and overall moral concern.