Federal regulators have ordered Google to assure employees they are allowed to speak out on political and workplace issues, people familiar with the matter say, as part of a settlement of formal complaints that the search giant punishes those who do just that.

The National Labor Relations Board’s move offers Google an escape hatch from a thorny issue that has roiled the business in recent years. Though Google executives have long bragged about having a workplace culture designed to encourage open debate, current and former...