Research Findings: This study examined processes of change associated with the positive preschool and kindergarten outcomes of children who received the Head Start REDI (REsearch-based, Developmentally Informed) intervention compared to usual practice Head Start. Using data from a large-scale randomized controlled trial ("N" = 356 children, 42% African American or Latino, all from low-income families), this study tests the logic model that improving preschool social-emotional skills (e.g., emotion understanding, social problem solving, and positive social behavior) as well as language/emergent literacy skills will promote cross-domain academic and behavioral adjustment after children transition into kindergarten. Validating this logic model, the present study finds that intervention effects on 3 important kindergarten outcomes (e.g., reading achievement, learning engagement, and positive social behavior) were mediated by preschool gains in the proximal social-emotional and language/emergent literacy skills targeted by the REDI intervention. It is important to note that preschool gains in social-emotional skills made unique contributions to kindergarten outcomes in reading achievement and learning engagement, even after we accounted for concurrent preschool gains in vocabulary and emergent literacy skills. Practice or Policy: These findings highlight the importance of fostering at-risk children's social-emotional skills during preschool as a means of promoting school readiness.