This study tested the authoritative school climate theory that schools characterized by high structure and student support have greater levels of student engagement and that these factors are associated with higher academic achievement, as indicated by school graduation rates and school performance on state-mandated testing. The model was tested through a multilevel multi-informant structural model on a statewide sample of 60,441 students and 11,442 teachers in 298 high schools. Consistent with the authoritative school climate model, both structure and student support were associated with higher student engagement in schools. Moreover, student engagement was directly associated with academic achievement and operated as an intervening factor. Results provide new evidence that an authoritative school climate is associated with high school academic achievement.