University success, which includes enrolment in and achievement at university, as well as quality of the university, have all been linked to later earnings, health and wellbeing. However, little is known about the causes and correlates of differences in university-level outcomes. Capitalizing on both quantitative and molecular genetic data, we perform the first genetically sensitive investigation of university success with a UK-representative sample of 3,000 genotyped individuals and 3,000 twin pairs. Twin analyses indicate substantial additive genetic influence on university entrance exam achievement (57%), university enrolment (51%), university quality (57%) and university achievement (46%). We find that environmental effects tend to be non-shared, although the shared environment is substantial for university enrolment. Furthermore, using multivariate twin analysis, we show moderate to high genetic correlations between university success variables (0.27-0.76). Analyses using DNA alone also support genetic influence on university success. Indeed, a genome-wide polygenic score, derived from a 2016 genome-wide association study of years of education, predicts up to 5% of the variance in each university success variable. These findings suggest young adults select and modify their educational experiences in part based on their genetic propensities and highlight the potential for DNA-based predictions of real-world outcomes, which will continue to increase in predictive power.