35-year-old Christopher Chaney of Jacksonville, Florida pleaded guilty in March to nine charges of unauthorised access to a computer and wiretapping.
Nude pictures of Johansson, 29, intended for her ex-husband Ryan Reynolds were subsequently published on the internet.
Prosecutors alleged that Chaney illegally hacked the email accounts of more than 50 people in the entertainment industry.
Chaney’s arrest by the FBI last August was part of a year-long investigation that has been dubbed "Operation Hackerazzi".
The investigation began in late 2010 as reports began to surface of celebrities' mobile phones and computers being hacked into.
Federal prosecutors are recommending a six-year prison sentence.