This study examined the relationships between first-year university students' academic motivation, retrospective evaluation of school experiences, subjective well-being, engagement and intention to drop out. Self-determination theory, the SInAPSi model of academic engagement, the hedonic approach, and the retrospective judgment process were used to frame the study. A final sample of 565 first-year Italian students enrolled in Science-Technology-Engineering-Mathematics (STEM) courses (Biology, Biotechnologies, Chemistry, Computer Science, Physics, Mathematics) was included. Three mediation models based on structural equations were tested to analyse the relationships between the proposed variables: motivation as an antecedent of dropout intention with only commitment as a mediator (model 1); model 1 + subjective well-being as a second mediator (model 2); model 2 + retrospective judgement as an antecedent (model 3). The results showed that in all models the more autonomous motivational styles predicted students' engagement, which in turn directly and indirectly influenced their intention to drop out. In model 2, subjective well-being acted as a mediator of the relationships between motivation, engagement and dropout intentions. In model 3, we found that subjective well-being also fully mediated the relationships between retrospective judgement and engagement. Overall, our findings provide new insights into the mechanisms underlying student engagement and dropout at university and may inform university policy.