Anne Longfield said children did not know how their data was being used due to "impenetrable" terms and conditions.
She said the internet was not designed for children even though they are now the biggest users.
She has called for a digital ombudsman to be created to uphold their rights.
'Give them power'
Despite the internet being an "incredible force for good", Ms Longfield said children were being left to fend for themselves with parents hoping they would avoid its pitfalls.
Her report also recommended that children should study "digital citizenship" to learn about their rights and responsibilities online and that social media companies should rewrite their terms and conditions in far simpler language.
Children already learn about using the internet and staying safe online at school as part of ICT but Ms Longfield wants to make this part of the curriculum from the age of four.
She said small print often contained "hidden clauses" waiving privacy rights and allowing content children posted to be sold on.
"Parents are always going to be on a losing battle which is why we need to take greater action to shift the balance of power towards children," she added.
"This is about helping children navigate this world, they have got all sorts of rights that we have signed up to in the physical world. It is now time to sign up to those in the digital world," she told Radio 4's Today programme.
Matteo is in year five.
He plays a game online where one person has to draw something while the other person guesses what it is.
"They couldn't guess what I drew and then someone called me an a-hole.
"I felt really upset so I straight away told my mum," he told Victoria Derbyshire.
Matteo's mum said she could do "absolutely nothing" about it.
"I blocked that person and I feel extremely guilty that he had had access to that."
"They just aren't aware of their digital footprint," she added.
The study tested teenagers' ability to understand the terms and conditions of photo-sharing website Instagram, which it says is used by 56% of 12 to 15-year-olds and 43% of eight to 11-year-olds.
The report said none of the teenagers understood fully what the terms and conditions committed them to.
The taskforce's panel then simplified and condensed Instagram's terms and conditions and found that the same group of children understood it easily.
After reading the re-written document, 13-year-old Alex, said he would delete Instagram because he thought it was "weird".
Another teenager, Ben, said it made him realise how much of his personal data he'd been giving away without realising.
A government spokesman said the UK was a "world leader in internet safety", but accepted there was more to do and that it would consider the report's findings.
He said: "The internet has given children and young people fantastic opportunities, but protecting them from risks they might face online or on their phones is vital."
Social media companies have to have robust processes in place to address inappropriate and abusive content on their sites, and they are expected to respond quickly to incidents of abusive behaviour on their networks.