Background Perfectionism, low self-esteem and external locus of control are psychological constructs linked to insomnia, anxiety and depression. Examining how these constructs impact mental health and serve as risk factors for the development of clinically significant symptoms may help direct psychological support resources and preventative measures for university students. Aims To longitudinally examine associations between the aforementioned psychological constructs and symptoms of insomnia, anxiety and depression in a large representative sample of first-year university students. Method Electronic surveys including validated measures of the predictors and outcomes were emailed to all first-year undergraduate students at entry to a major Canadian university, and followed up on at conclusion of the academic year. Results Compared with healthy sleepers, students screening positive for insomnia had lower self-esteem, higher self-evaluative perfectionism and increased external locus of control (all P < 0.001). Self-evaluative perfectionism (standardised β = 0.13, P < 0.01), self-esteem (β = −0.30, P < 0.001) and external locus of control (β = 0.07, P = 0.02) measured at entry were significantly associated with insomnia symptoms at follow-up. Insomnia symptoms at entry were strong predictors of symptoms of depression (β = 0.15, P < 0.001) and anxiety (β = 0.16, P < 0.001) at follow-up, even after controlling for baseline symptoms of those disorders. Conclusions Perfectionism, low self-esteem and external locus of control may predispose the development of insomnia symptoms in university students. In turn, insomnia symptoms appear to be robust predictors for depressive and anxiety symptoms. Sleep may be an important prevention target in university students.