The management of digital innovations represents a major challenge for organizations, because they evolve in non-linear, reflexive, and distributed ways. Since digital innovations’ logic is so different, the demands regarding institutionalized anchoring of the innovation management function may be substantially different. However, there has been little attention to organizational design’s role aimed at building appropriate structures to accommodate digital innovation management. Drawing on the organizational information-processing theory, we address this gap by proposing a conceptual framework to understand the interplays between organizational design and digital innovations’ logic. Our framework proposes that, depending on their combination with others, organizational design strategies may have either positive or negative effects on digital innovation performance, and that they may appear in configurations that exhibit high and low performance. It further suggests that while the general ability to innovate is context-specific, multiple configurations of strategies may be equally effective in the same setting. Our paper contributes to the field, since it enables us to achieve a theoretically framed understanding of a key contemporary phenomenon and helps us to identify ideal-type configurations of digital innovation management.