Drawing on social exchange theory, we developed and tested a cross‐level model of organizational‐level predictors of job engagement. Specifically, we examined the impact of high‐performance human resource (HR) practices on employee engagement and work outcomes. Based on a sample of 605 employees, their immediate supervisors, and HR managers from 130 companies, our results indicated that high‐performance HR practices were directly related to job engagement as well as indirectly related through employees' perceived organizational support. In turn, job engagement was positively related to in‐role performance and negatively related to intent to quit. Culture was found to act as a critical contextual factor, as our results also revealed that the relationship between HR practices and perceived organizational support was stronger when collectivism was high and when power distance orientation was low. Overall, the findings shed new light on the processes and conditions through which employee work‐related outcomes are enhanced owing to high‐performance HR practices. Copyright © 2015 John Wiley & Sons, Ltd.