Empirical findings concerning the effects of extrinsic rewards on employee creativity have been controversial and have focused mainly on the theoretical mechanism of intrinsic motivation. Although intrinsic motivation is a primary impetus for creativity, generating creative outputs is a process that requires a sequence of creative endeavors. Drawing from the componential theory of creativity, this study proposes a positive relationship between extrinsic rewards and creativity via creative process engagement. Additionally, two types of employee characteristics, i.e. person-job fit and cognitive flexibility, are important contingency factors affecting the reward–creativity relationship. Our empirical analyses of data collected from 228 supervisor-subordinate dyads demonstrate the mediating role of creative process engagement in the reward–creativity relationship. Moreover, employees with high levels of person-job fit and cognitive flexibility are found to have the highest levels of creative process engagement and, in turn, the greatest creativity when motivated by extrinsic rewards for creativity. These findings have several theoretical and managerial implications related to reward–creativity research and practice.