A newly discovered data breach exposed the private information of more than 1 billion Yahoo users, the company said, dwarfing the scope of another recently disclosed hack and casting doubt on Verizon Communications Inc.’s planned acquisition of the internet company.

The 2013 theft is separate and twice as large as a 2014 hack that Yahoo Inc. disclosed earlier this year. That hack had been billed as likely the largest-ever theft of personal data.

Unidentified...