Facebook messages in the name of "Brian Kil" were sent to the girls, using the Tor anonymising network, from 2012.
They threatened to kill them and their families or blow up their schools if they did not share explicit images.
The FBI says it tricked "Brian Kil" into viewing a video bearing virus-like code that logged his real net address.
Buster Hernandez has been charged with several counts of sexual exploitation of a child, threatening to use explosives and threatening to injure.
Mr Hernandez has yet to enter a plea.
If convicted, he faces a mandatory minimum sentence of 15 years in jail.
The Facebook messages claimed "Brian Kil" had already accessed explicit pictures the girls had previously shared, which he would publish unless they sent him more.
In at least three cases, the messages claimed the sender would also visit the girl's school and use pipe bombs and guns to kill her and her friends.
Two schools were closed for 24 hours while police investigated these threats.
The Tor anonymising network hides a person's identity by bouncing requests for data through many different computers.
And messages excerpted in the court documents show "Brian Kil" taunting investigators for their inability to track him down.
But after local police in Indiana called on the FBI for help investigating the case of two victims who lived in the state, agents added extra code to one video file uploaded along with other images to a private Dropbox account.
And when this video was viewed, the code grabbed the IP address of Mr Hernandez's computer, the FBI alleges.
"Mr Hernandez's reign of terror is over," said US Attorney Josh Minkler in a statement.
"Those who think they can outwit law enforcement and are above being caught should think again."
The FBI has charged an American man officers believe to be behind an online extortion campaign to make young girls share explicit pictures of themselves.