Understanding how parents shape their children’s educational trajectories is a socially important research goal. Evidence on the effects of parents’ cognitive and non-cognitive skills on offspring education is weakened by poor assessments of non-cognitive skills and inadequate accounting for genetic inheritance. In this preregistered study, we use genetics to assess non-cognitive skills and to index environmental effects of parents, controlling for direct effects of inherited genetic variation. We define the non-cognitive and cognitive heritable contributions to educational attainment using GWAS-by-subtraction, and construct non-cognitive and cognitive skills polygenic scores in three UK and Dutch cohorts. We estimate environmentally mediated effects of polygenic scores (parental indirect genetic effects) on educational achievement and attainment with three designs that include siblings (N=47,459), adoptees (N=6,407), and parent-offspring trios (N=2,534). Heritable non-cognitive and cognitive skills are both involved in parental construction of environments influencing offspring education: indirect genetic effects explain ∼37% of total polygenic score effects. This result holds across countries, outcomes, ages and methods, with two exceptions: indirect genetic effects are null for childhood achievement in the Dutch cohort, and lower when estimated with the adoption method. Overall, our findings stress the importance of both non-cognitive and cognitive aspects of the home environment.