Stenson entered his guilty plea at a case management hearing.
His plea follows an investigation by Operation Pinetree - the police inquiry into the features desk at the paper.
His co-defendant Neil Wallis, the News of the World's former deputy editor, pleaded not guilty.
Mr Wallis is expected to go on trial next June.
Both men were accused of conspiring to illegally listen to voicemails with Andy Coulson, Greg Miskiw, James Weatherup, Neville Thurlbeck, Dan Evans, Ian Edmondson, Glenn Mulcaire and others unknown between January 2003 and January 2007.
The other individuals named aside from Stenson and Mr Wallis were charged under the Metropolitan Police's main phone-hacking investigation, Operation Weeting.
The trial of two former News of the World editors, Rebekah Brooks and Andy Coulson, heard that Stenson set up a phone-hacking operation on the features desk to rival that run by the news desk.
Mrs Brooks was found not guilty of phone-hacking charges. Coulson was found guilty of conspiracy to intercept phone messages and served five months in prison.
Reporter Dan Evans, who admitted phone hacking, gave evidence during their trial that Stenson employed him specifically to do "stuff with phones".
The former features editor of the News of the World, Jules Stenson, has pleaded guilty at the Old Bailey to conspiring to hack phones.