News International is apologising and offering compensation after a UK tabloid newspaper, The News of the World hacked into the mobile phones of celebrities.
Earlier this week, a reporter and an ex-news editor of the paper were arrested in connection with the case.
The BBC's business editor said News International was offering to settle with eight people and the payments could cost the company £20 million.
News International said the announcement related to interception of voicemails between 2004 - 2006.
The company said it would continue to co-operate with an inquiry by the Metropolitan Police in London.
Former Sunday Times editor Andrew Neil said it was a "complete mea culpa".