The hackers, all students between the ages of 15 and 23, began their attacks last July during the G8 summit in Genoa. Police said hackers placed the slogan "Hi-Tech Hate" on Web sites.
The group attacked US government sites included those of the Pentagon, NASA and several courts and universities including Harvard, Columbia and Cornell, police said.
Government Web sites in the UK, China, Sweden, Portugal, Australia, Bolivia, the Philippines, Mexico, Ecuador, Venezuela, Pakistan and Bahrain also came under attack.
In Italy the group hacked health and defence ministry Web sites, and also attacked sites belonging to the Senate, media organisations, the Internet provider Italia On Line, the Democratic Party of the Left, and pop singer Claudio Baglioni.
The Italian police force's Anti-Technological Crime Unit (GAT) handled the investigation, which began last August, following the discovery of an attempted hack into a software company's Web server.
Investigators followed the trail to a Hi-Tech Hate hacker and subsequently tracked down the other five. The students lived in different parts of Italy and kept in contact via the Internet, investigators said.
"This was one of the most prolific hacker groups ever seen in terms of the number of its attacks. They were very expert," said Giancarlo Samele, a member of the GAT. "We don't have an estimate of the financial damage caused, but it should not be very high," he added. "These were not really malicious attacks."
According to Gianluigi Chiapponi, the prosecuting solicitor in charge of co-ordinating the case, the hackers are likely to escape with suspended prison sentences because they have no previous convictions, and their attacks did not cause serious damage.