A pragmatic “holy grail” of organizational aspirations, ambidexterity is increasingly gaining the attention of executives and scholars alike, presenting them with a frame of thought and a functional strategic attitude that befits the perplexing nature of contemporary business contexts. Aiming to cover one of the most noticeable gaps in knowledge on the subject, this exploratory research studies the evolutionary process of a divisional multi‐business‐unit organization to an ambidextrous one. We thus identify the determinants of a successful evolution and propose an executive‐oriented comprehensive model towards divisionalized ambidexterity. In this context, we answer critical questions relating to the relative weight of innovation within multiunit business ambidexterity, the requisite means and aims of the structural and contextual determinants of success, and the role of top management. We conclude that there is a strategic need for balance between internal and external congruence; and that multiunit integration must be such as to achieve an internal solidification of systems and processes, as well as external adaptability and market flexibility; all within an incessantly changing and unpredictable business environment. The value of the research to human resource management knowledge lies in its focus on multiunit business ambidextrous evolution; and in its consequential scientifically founded practical elucidations of executive worth. Equally importantly, though, the findings transcend theoretical constrictions to provide an in‐context business perspective through a comprehensive system that considers also strategic and environmental realities. © 2015 Wiley Periodicals, Inc.