Identifying the cognitive capacities associated with the development of school readiness is indispensable to support children's successful school transition. It has been shown that executive function (EF) in preschoolers is associated with both concurrent preacademic and subsequent academic skills. However, most research has controlled for the effect of general cognitive ability (GCA), and little research has examined non-English speaking children, which hinders the understanding of the development of school readiness in culturally diverse contexts. In addition, behavioral genetic research on the genetic and environmental influences on this association has been conducted with school-age children. Thus, the genetic and environmental influences on associations between GCA, EF, and preacademic skills during preschool age are unknown. We conducted multivariate behavioral genetic analyses on two waves of longitudinal data at 42 and 60 months of age from 171 and 135 pairs of monozygotic and dizygotic Japanese twins. The findings suggested that a genetic factor influenced GCA at 42 months and mediated preacademic ability at 60 months. In addition, another genetic factor emerged by 60 months that genetically mediated EF and math ability, independent of GCA. Preacademic ability at 60 months was affected by shared environments that influenced EF, rather than GCA, at 42 months. Moreover, shared environments that influenced preacademic ability at 42 months affected later GCA at 60 months. Finally, nonshared environments that had emerged by 60 months mediated these relationships, though the magnitude of this effect was modest.