Research has shown that work engagement, both at the individual and team levels, is relevant to understand employee performance and well‐being. Nonetheless, there is no theoretical model that explains the development of work engagement in teams that takes into consideration what is already known about team dynamics and processes. This study addresses this gap in the literature, presenting a model for the emergence of team work engagement. The model proposes team inputs, outputs, and mediators as predictors of team work engagement and highlights their recursive influences over time. This conceptual work provides a starting point for further research on team work engagement, allowing for distinguishing individual and team constructs. Practitioner points The degree of energy and enthusiasm of teams depends on the way they interact. The affective and motivational dynamics of teams have consequences for their performance and well‐being. The emergence of team work engagement is better understood within the literature of teamwork.