Digital transformation has intensified the pressure on firms to improve operational efficiency while simultaneously generating strategic renewal. Firms are expected to automate routine processes, reduce costs, improve reliability, and scale digital operations without losing the capacity to experiment, innovate, and create new sources of competitive advantage. This dual demand creates a central theoretical problem for business management. Operational automation and strategic innovation are both enabled by digital technologies, yet they rely on different organizational logics, resource commitments, governance routines, and managerial capabilities. This article develops a theory of digital ambidexterity to explain how firms balance operational automation and strategic innovation under resource constraints. It argues that digital ambidexterity differs from general organizational ambidexterity because digital technologies are not merely tools that support exploitation and exploration but also reshape the tension between them. The article uses a theory-building synthesis of peer-reviewed journal articles published. It integrates ambidexterity theory, digital transformation research, dynamic capabilities, resource-based logic, automation studies, and digital innovation scholarship to construct a conceptual model and derive testable propositions. The proposed theory identifies operational automation and strategic innovation as distinct but interdependent digital logics. Firms that balance these logics can achieve both efficiency and renewal, whereas firms that overemphasize automation risk rigidity and firms that overemphasize innovation risk fragmented experimentation and resource dissipation.