Equifax Inc. moved to take concrete action over its massive hack ahead of congressional hearings next week, announcing Tuesday that Chairman and Chief Executive Richard Smith would step aside while leaving the door open to compensation clawbacks.

The credit-reporting company’s board looked to show Equifax and its leadership were being held accountable for the breach, according to people familiar with the matter. Equifax on Sept. 7 disclosed that the cyberattack compromised vital personal information—names, addresses, social...