We constructed a model of workplace psychosocial safety climate (PSC) to explain the origins of job demands and resources, worker psychological health, and employee engagement. PSC refers to policies, practices, and procedures for the protection of worker psychological health and safety. Using the job demands–resources framework, we hypothesized that PSC as an upstream organizational resource influenced largely by senior management, would precede the work context (i.e., job demands and resources) and would in turn predict psychological health and work engagement via mediation and moderation pathways. We operationalized PSC at the school level and tested meso-mediational models using two-level (longitudinal) hierarchical linear modelling in a sample of Australian education workers (N = 209–288). Data were repeated measures separated by 12 months, nested within 18 schools. PSC predicted change in individual psychological health problems (psychological distress, emotional exhaustion) through its relationship with individual job demands (work pressure and emotional demands). PSC moderated the relationship between emotional demands and emotional exhaustion. PSC predicted change in employee engagement, through its relationship with skill discretion. The results show that the PSC construct is a key upstream component of work stress theory and a logical intervention site for work stress intervention.