Background/Objectives: Schools can play a key role in promoting health among adolescents, and Hungarian legislation gives them sufficient space to do so. In our study, we examined the impact of a multiyear school health promotion programme on pupils’ health behaviour and well-being. Methods: We carried out our investigation in an intervention and a control primary school in Hungary. All 5th and 7th grade pupils were invited to participate in the questionnaire-based survey between 2017 and 2021. The effect of the intervention was quantified using univariate and multivariate logistic regression analyses. Results: Our results show that for those behaviours where pupils’ personal choices had a greater influence (unhealthy eating, smoking, screen time), the health promotion programme was more effective. For those behaviours where family background and parental influence were more pronounced (healthy eating, physical activity), the intervention had less impact. Self-perceived health was better in the 7th-grade intervention group. Conclusions: Our findings are in line with the conclusion of systematic reviews that more intensive, longer-term, multi-behavioural school health promotion programmes can be effective in promoting positive behaviour. To be more effective, it would be worth using a well-structured curriculum, well-developed teaching materials, and greater involvement of teachers, parents, and various local organisations.