The US authorities say Ryan Collins has agreed to plead guilty to the offence.
Prosecutors have recommended that he face a jail term of 18 months, although a judge could extend that to five years.
The 36-year-old is alleged to have stolen usernames and passwords via a phishing scam.
The BBC reports that the Department of Justice said that Pennsylvania-based Collins had admitted to breaking into more than 100 accounts between November 2012 and September 2014.
He is said to have achieved this by sending emails to the victims that pretended to be from Google or Apple requesting their login details.
“[The] defendant used numerous fraudulent email addresses designed to look like legitimate security accounts from various internet service providers, including, for example,
Collins is accused of accessing at least 50 iCloud accounts and 72 Gmail accounts.
Once he had fooled their owners into handing over their details, prosecutors say, he searched through the victims’ online data.
“Through his phishing scheme [the] defendant was also able to access full Apple iCloud back-ups belonging to numerous victims, including at least 18 celebrities, many of whom reside in the Los Angeles area,” the court papers state.
“Many of these back-ups contained nude photographs and videos.”
The celebrities are not named, but the attacks coincide with stolen photos of the actresses Jennifer Lawrence, Kate Upton, Mary Elizabeth Winstead and others being posted to the internet in 2014, which was blamed on an iCloud breach at the time.
Collins has not been accused of uploading the images for others to see.
“By illegally accessing intimate details of his victims’ personal lives, Mr Collins violated their privacy and left many to contend with lasting emotional distress, embarrassment and feelings of insecurity,” said David Bowdich, the assistant director in charge of the FBI’s Los Angeles field office.
“We continue to see both celebrities and victims from all walks of life suffer the consequences of this crime and strongly encourage users of internet-connected devices to strengthen passwords and to be sceptical when replying to emails asking for personal information.”
The FBI added that the case against Collins was part of an “ongoing investigation”, indicating that there may be further arrests.
