Prosecutors had accused Jared James Abrahams of carrying out the attacks over a two-year period.
The current winner of the Miss Teen USA beauty pageant - Cassidy Wolf - had been identified as one of his targets.
The 19-year-old computer science student will be sentenced in March.
He faces up to 11 years in jail and $1m (Â£626,000) in fines.
According to prosecutors, at least two dozen women in the US, Ireland and elsewhere had their PCs hacked by Abrahams.
Court records state that the computer science student told the women - who ranged from the age of 16 to their early 20s - that he had taken pictures of them while they were undressed. He then threatened to post the images to social media sites unless they sent additional photos or stripped via a Skype video feed.
The authorities said at least two of the victims had complied.
Cassidy Wolf - a schoolmate of Abrahams - did not respond to his threats.
Abrahams later posted a naked photo of the beauty queen online and is reported to have sent her a message saying: "Your dream of being a model will be transformed into a porn star."
Appearing in court at Santa Ana, California, he pleaded guilty to three counts of extortion and one count of unauthorised computer access.
He also told the judge that he had autism - a factor his lawyer said should be taken into account when sentencing takes place.
The case is not the first of its kind.
In July another American, Karen "Gary" Kazaryan, pleaded guilty to hacking into women's computers, stealing their online identities and then using them to fool other women into removing their clothing on camera.
The previous year the US courts convicted Trevor Timothy Harwell for installing spyware on women's laptops and then sent an alert stating that they needed to place the machines "near hot steam" to fix an internal sensor. Many of the women took the machines to their bathrooms to do so, where he took photos of them getting undressed.
The charity, Childnet International, has become so concerned by such threats that in June it suggested webcams should be disconnected when not in use.
Cassidy Wolf posted a similar message in a tweet after Abrahams pleaded guilty: "Happy to know that this nightmare is coming to an end #ProtectYourselves #CoverYourWebcams."
A US teenager has pleaded guilty to hacking into the computers of young women, using their webcams to take photos, and then threatening the victims with blackmail.