Emotional exhaustion and depression pose a threat to employees' psychological health. Social relationships at work are important potential buffers against these threats, but the corresponding psychological processes are still unclear. We propose that the subjective experience of high‐quality relationships with supervisors (i.e., Leader–Member Exchange [LMX]) is one of the protective factors against psychological health issues at work and that this effect is mediated by psychological empowerment. We tested these assumptions with two studies (one cross‐sectional and one time lagged) on diverse samples of employees from different organizations. The first study employed emotional exhaustion as the outcome measure; the second used depression. Results from both studies support the proposed process by showing that LMX positively affects empowerment, which negatively affects emotional exhaustion (Study 1) and depression (Study 2). Additionally, Study 2 also showed that Team–Member Exchange is as important as LMX for preventing psychological health issues among employees. Copyright © 2015 John Wiley & Sons, Ltd.