Being promoted over your coworkers is a tricky situation. It’s important to get off on the right foot with your former peers and to make the transition as smooth as possible. Ideally, the team will learn about your promotion from someone else. But if you have to make the announcement yourself, be modest with the wording. This isn’t the time to toot your own horn. Don’t let people make assumptions about what your new relationship will be like — show them. Meet with each team member one-on-one. If you competed with a peer for the job, pull them aside to say you value their contributions. Take a specific action to back up your words, such as assigning them to an important task. And don’t introduce any sweeping changes right away. No matter how good your plan is, hold off until you’ve established your credibility as a manager.
Adapted from The Harvard Business Review Manager's Handbook: The 17 Skills Leaders Need to Stand Out