Lord Richard Best of the Lords Communications Committee said that the internet is hugely beneficial but that children need to be aware of its dangers.
The report also suggested that digital literacy was as important as reading, writing and arithmetic.
Lord Best also argued that it was important to help young people become "empowered, digitally confident citizens."
Clive Ireson -- from the Association of Christian Teachers told Premier he gave the report a cautious welcome.
"It's good news really. How we're going to achieve that I'm not sure but it does need to be done. The curriculum does need to change over time because technology is ever changing."
The report also recommended that online businesses should respond more quickly to requests by children to remove inappropriate content.
Ireson told Premier that tech companies have a moral responsibility to do their bit.
"These are the companies that have the money and technology is available now that if it was being put into 'phones as they are built it would allow parents to know what sites their children are on," Ireson said.
A government spokesperson said they would "carefully consider the recommendations included in the Lords Communications Committee Report".