James Murdoch, who heads the newspaper's European operations, says the 168-year-old newspaper will publish its last edition Sunday. The scandal has cost the paper prestige and prompted dozens of companies to pull their ads.
The Rupert Murdoch-owned tabloid is accused of hacking into the cell phone messages of victims ranging from missing schoolgirls to grieving families, celebrities, royals and politicians in a quest for attention-grabbing headlines.
Police say they are examining 4,000 names of people who may have been targeted by the paper.
The Sunday-only newspaper has acknowledged that it hacked into the phones of politicians, celebrities and royal aides, but in recent days the allegations have expanded to take in the phones of missing children, the relatives of terrorist victims and families of soldiers killed in Afghanistan.
James Murdoch said if the allegations were true, "it was inhuman and has no place in our company."
"Wrongdoers turned a good newsroom bad," he said, "and this was not fully understood or adequately pursued."