LONDON—Prosecutors on Tuesday charged Rebekah Brooks, the former head of News Corp.'s British newspaper unit, with conspiring to obstruct justice, marking the first criminal charges filed in a wide-ranging criminal investigation at the media company's U.K. tabloids.

Ms. Brooks and five others were charged by the Crown Prosecution Service with "conspiracy to pervert the course of justice" by impeding a criminal investigation probing phone hacking and alleged bribery of public officials at the company's tabloids, the News of...