Teacher-student relationships (TSRs) are positively related to students' academic engagement across different countries. However, the mediation mechanism between TSRs and academic engagement remains unclear, and research is needed to completely understand this association. Therefore, the present study aimed to investigate the association between TSRs and academic engagement and the mediating role of basic psychological needs satisfaction. A sample of 494 primary school students in China completed self-reported questionnaires on TSRs, basic psychological needs satisfaction, and academic engagement. The results showed that TSRs were positively associated with academic engagement (behavioural, emotional, and cognitive engagement). Moreover, the satisfaction of the need for autonomy was a mediator between TSRs and emotional and cognitive engagement, but not behavioural engagement; TSRs were related to the students' three subdimensions of engagement through the need for relatedness; the need for competence was a mediator only between TSRs and behavioural engagement, but not emotional and cognitive engagement. These results help uncover the mechanisms behind the role of TSRs on academic engagement.