We investigate the impact of vaccination and asymptomatic testing uptake on SARS-CoV-2 transmission in a university student population using a stochastic compartmental model. We find that the magnitude and timing of outbreaks is highly variable under different vaccine uptake levels. With low level interventions (no asymptomatic testing, 30% vaccinated), 53-71% of students become infected during the first term; with high interventions (90% using asymptomatic testing, 90% vaccinated) cumulative incidence is 7-9%, with around 80% of these cases estimated to be asymptomatic. Asymptomatic testing is most useful when vaccine uptake is low: when 30% of students are vaccinated, 90% uptake of asymptomatic testing leads to almost half the case numbers. Under high levels of vaccine uptake (70-90%), case numbers in the student population are largely driven by community importation. Our findings suggest that vaccination is critical for controlling SARS-CoV-2 transmission in university settings with asymptomatic testing being a useful supporting measure.