Several studies show the need to investigate the psychological processes involved in university dropout. The study aimed to estimate the influence of perceived autonomy support and academic self-efficacy perception on the intention of permanence of university students, evaluating the mediating role of academic satisfaction. The participants were 273 first-year students from a private university in Bio Bio, Chile. The influence of cognitive-motivational factors was assessed through path analysis. The mediating effect was evaluated through the Mplus program. Results show that academic satisfaction fully mediates the effect of the perceived autonomy support and the perception of academic self-efficacy on the intention of permanence. It is concluded that the positive levels of academic satisfaction positively influence the intention to continue studying a university degree.