Three Russian companies and 13 Russian citizens were indicted Friday on charges of engaging in a widespread effort to interfere in the 2016 presidential election, providing the most comprehensive official account to date of a sweeping, multimillion-dollar effort by Russians to upend U.S. politics.

The indictment, secured by special counsel Robert Mueller in his investigation into whether Russia meddled in the campaign, alleges that Russians wielded social-media messages, invented fake personas and staged rallies with the “strategic...