Abstract One important question in public‐private (PP) projects is how to manage coopetition—simultaneous cooperation and competition among project members. Prior studies on the governance of PP projects showed the importance of governance mechanisms to deal with major events such as technical or organizational disruptions but paid limited attention to the management of coopetition. At the same time, research on the management of coopetition mostly focused on industrial coopetition, whereas PP projects also entail public‐private coopetition. Seeking to better understand how governance mechanisms may help manage coopetition in PP projects, we conducted an in‐depth study of Galileo—a large PP project aimed at delivering Europe's own satellite‐based navigation system. The findings show how three core aspects of project governance—(i) mechanisms (joint vs. separate use of contractual and relational mechanisms), (ii) form (lead organization vs. shared governance), and (iii) goals (to promote cooperation and/or prevent competition)—jointly explained the emergence and (mis)management of knowledge‐ and value‐related coopetitive tensions. In turn, these tensions prompted a series of adaptations in the governance of the project. Our study contributes to a co‐evolutionary understanding of the governance of PP projects and offers implications for practitioners seeking to (re)design PP project governance.