Facebook Inc. is close to a settlement with the U.S. government over charges that it misled users about its use of their personal information, the latest sign of widening public concern over privacy in the digital age.

According to people familiar with the talks, the settlement would require Facebook to obtain users' consent before making "material retroactive changes" to its privacy policies. That means that Facebook must get consent to share data in a way that is different from how the user originally agreed the data could...