In light of the workforce's increasing nationality diversity, our study explores the antecedents for the successful management of nationality diversity as visualized in a favourable diversity climate and enhanced team performance. We propose a double‐contingency model in which we argue that the effects of nationality diversity will be dependent upon task interdependence and leaders’ cultural intelligence. We propose that nationality diversity will be more consequential in more interdependent teams, in which team interactions and processes are more salient. Moreover, team leaders with higher cultural intelligence will possess the skills to foster adequate team processes and thereby enhance diversity climate and performance of nationally diverse, more interdependent teams. We collected multi‐source data from 63 work teams (N = 410) and their supervisors at a German facility management company. Moderated regression analyses supported the hypothesized three‐way interaction between nationality diversity, task interdependence and leaders’ cultural intelligence. Additional simple slope analysis showed that nationality diversity is positively related to diversity climate and performance only when both team leaders’ cultural intelligence and task interdependence are high. Our study not only provides recommendations for successful nationality diversity management but also yields theoretical implications for diversity and cultural intelligence research.