Under the proposed law, owners of a website - including blogs and social media accounts - have 48 hours to remove offensive content before legal intervention from Italy's Garante della privacy, the official institution in charge of protecting personal data.
Site moderators who fail to remove the offending content would face a fine, while those found guilty of cyber stalking or bullying, such as posting offensive content and circulating demeaning or offensive photos or videos, could be jailed for up to six years.
The law has been in the making for over a year, following several cases of teenagers killing themselves following online mockery.
Its approval in the Chamber of Deputies comes days after Italy's privacy tsar ruled that an Italian court had been wrong not to consider the online publication of a sex tape an illegal breach of privacy. The woman, Tiziana Cantone, moved cities and changed her name to escape the humiliation before killing herself this month.
Democratic Party senator Elena Ferrara put forward the first draft of the law following the suicide of 14-year-old Carolina Picchio in January 2013. Picchio had been the victim of cyber bullies who had circulated an offensive video.
The law was approved on Tuesday with 242 votes in favour, 73 against and 48 abstentions, and will now be passed back to the Italian Senate for final approval.
The majority of the votes against came from the Five Star Movement. Beppe Grillo's populist party criticized amendments to the law as a step in the direction of censorship, due to the fact that anyone can demand the removal of content they deem "mocking" or "insulting", without the need for an objective third party judgment.
A statement from the party declared that “a good law” had been “sabotaged” in the chamber, and that minors had been "sacrificed on the altar of censorship".
They expressed hope that the Senate, which has approved the law in its original form - with a focus on informing school pupils about cyber bullying and empowering victims, rather than punishment - would now undo these changes.
However, other political parties greeted the move. "We are seeing and living stories of terrible violence, including psychological violence, on an almost daily basis, which are born and spread on the web," Ettore Rosato from the Italian Democratic Party said in a Facebook post. "It is our duty to intervene."
Non-profit organization Telefono Azzurro said it received calls about bullying, including cyber-bullying, on a daily basis in the last school year. The majority of incidents involved young teens aged between 11 and 14.
Ernesto Caffo, president of the organization, said the law's approval was "a very positive sign," La Repubblica reported.
"We trust that today's approval will finally lead - after the law's passage to the Senate - to a law against the phenomenon of bullying and cyber bullying; a law which Telefono Azzurro has always supported vigorously," said Caffo.
The text includes the first legal definition of what constitutes bullying and cyber bullying, and also sees the Ministry of Education and schools taking a key role in prevention and tackling of bullying.
The Ministry of Education has also been tasked with developing official ‘guidelines' to deal with cyber bullies, and every school will appoint a dedicated ‘anti-bullying' teacher, responsible for informing the families of all those involved in cases of bullying.