Grounded in achievement goal theory and basic psychological needs theory, the aim of this study was to examine the impact of the interaction of perceived motivational climate in physical education with psychological needs satisfaction (relatedness, competence and autonomy) and psychobiosocial states on student intention to engage in leisure-time physical activity. Participants (N = 470 Italian students, 287 boys and 183 girls, aged 16–19 years) completed the Teacher-Initiated Motivational Climate in Physical Education Questionnaire, the Psychological Needs Satisfaction Scale in Physical Education, the Psychobiosocial States Questionnaire, and a measure of intention to engage in leisure-time physical activity. Structural equation modelling analysis indicated that a perceived task-involving climate was related to intention to engage in physical activity through the serial mediation of competence need satisfaction and pleasant/functional psychobiosocial states. The findings highlight the importance of task-involving climate and competence need satisfaction in determining pleasant emotional states and, consequently, in promoting leisure-time physical activity. Teachers should apply curricular and pedagogical strategies that aim to create a task-involving motivational climate, make movement experiences personally meaningful and pleasant and therefore stimulate students to adopt an active lifestyle.