Erasmus+ is one of the most popular programmes financed by the European Union. It provides international mobility grants to university students while staying enrolled at their home university. This paper brings novel evidence on the effect of participating in the programme on students' academic outcomes, using rich administrative data from one of the largest public universities in Italy. We rely on a fuzzy Regression Discontinuity Design, since the selection of applicants to Erasmus mobility programmes depends on a continuous score assigned during the application process. Our results show that Erasmus mobility does not delay graduation at the home university and, in addition, it has a positive and significant impact on undergraduates' final degree mark. Investigating possible heterogeneous effects, we find that Erasmus mobility improves graduation results for undergraduate students in scientific and technical fields (STEM) and for those who apply for the Erasmus grant in the first year of their studies. Finally, the positive impact on performance at graduation appears to be stronger for students who visit foreign universities of relatively lower quality compared with their home university and for those who stay abroad for more than six months.