Andreas Dowling, 24, targeted Allerton High School, St Mary's Catholic School, Cockburn High School, Temple Moor High School, Leeds East Academy and John Smeaton Academy in West Yorkshire, as well as schools and colleges across Britain, the United States and Canada.
He also made threats to the Palace of Westminster, police stations and the Super Bowl.
Dowling, of Carew Terrace, Torpoint, appeared at Bristol Crown Court on Thursday where he admitted 31 charges relating to 107 offences dating back to 2014.
He was caught following an internal investigation led by Counter Terrorism Policing who teamed up with the FBI and officers in Michigan.
A total of 75 schools and colleges fell victim to the hoaxes in January and February 2016, but the investigation between the different agencies uncovered many earlier offences committed by Dowling in the US.
Dowling - who used software to disguise his voice when making the hoax calls - was a member of a small online group which claimed responsibility for a campaign of bomb threats across the world in 2016, causing substantial disruption to the education of tens of thousands of pupils and sparking major policing responses in the affected areas.
“I hope this will serve as notice to anyone who considers such acts in the future that no matter how long it takes, or how far we have to travel to gather evidence, we will find you. You may think that technology will protect you but it will also help us track you down."
Counter Terrorism Police picked up the investigation after a school in Cornwall and several in Bristol were the first to be targeted.
After becoming aware of similar hoaxes taking place in the US around the same time, investigators made contact with the FBI and together they identified Dowling as a suspect.
Following a search of his home and digital devices, it was revealed Dowling owned an eBook which included chapters about making bomb threats to high schools and another providing instructions about how to send armed response officers to someone’s house. He also had a file titled ‘bomb threats by email’.
“The hoaxes had a profound effect upon the schools and colleges affected, creating a culture of anxiety and fear amongst the pupils. It was therefore vitally important we brought those responsible to justice, irrespective of the length of time it took.
“Dowling tried to use computer software to hide both his identity and the sheer scale of his offending, but with the assistance of the FBI and a number of US law enforcement agencies we were able to build our case against him.
“Such was the weight of evidence, Dowling had little choice but to admit to causing chaos and distress to his victims worldwide.”
Dowling will be sentenced at the same court on December 2.