A polygenic risk score (PRS) for attention-deficit/hyperactivity disorder (ADHD) has been found to be associated with ADHD in multiple studies, but also with many other dimensions of problems. Little is known, however, about the processes underlying these transdiagnostic associations. Using data from the baseline and 1-year follow-up assessments of 9- to 10-year-old children in the Adolescent Brain Cognitive Development™ (ABCD©) Study, associations were assessed between an ADHD PRS and both general and specific factors of psychological problems defined in bifactor modeling. Additionally, prospective mediated paths were tested from the ADHD PRS to dimensions of problems in the follow-up assessment through baseline measures of executive functioning (EF) and two facets of impulsivity: lower perseverance and greater impulsiveness in the presence of surgent positive emotions. Previous findings of modest but significant direct associations of the ADHD PRS with the general factor of psychological problems were replicated in both assessments in 4,483 children of European ancestry. In addition, significant statistical mediation was found from the ADHD PRS to the general factor, specific ADHD, and conduct problems in the follow-up assessment through each of the two facets of impulsivity. In contrast, EF did not statistically mediate associations between the ADHD PRS and psychological problems. These results suggest that polygenic risk transdiagnostically influences both psychological problems and facets of impulsivity, perhaps partly through indirect pathways via facets of impulsivity.