The right to delete embarrassing and sometimes incriminating posts from the internet will allow children to become adults without their childhood leaving a permanent mark on the web.
It would also mean that they could take responsibility, as adults, by deciding to remove any regrettable data.
Launching the new iRights framework aimed at working towards better protection for young people online, its founder and crossbench peer Baroness Beeban Kidron said that those under 18 should be given the right to mature freely.
A series of rights for under-18s have been proposed in order to ensure that they are able simply request the removal of any unwanted content.
The iRights plan wants websites to feature a delete button to enable this.
It also wants children to have the right to know, the right to safety and support, the right to informed and conscious choices, and the right to digital literacy.
Baroness Kidron said: "Young people mature, they say things they regret and so on. It is often centred around the issue of transgression.
"There is something more profound about development - the right to be who you are, at any given point.
"The idea that you can create your present self is a very very important part of becoming an adult and it is not about not taking responsibility.
"It is about taking responsibility for who you currently are.
"People develop between the ages of 0 and 18, they become adults and we should be encouraging experimentation and change."
She added that rather than giving young people a safety net, it would actually cause them to think twice about posting something which they might later want to delete.
Baroness Kidron continued that it was also very important for young people to be aware of the scale of data gathering that goes on.
Businesses and groups with a digital footprint are being urged to enshrine a universal standard of rights into their digital services and communications to help protect and inform young people online.
Baroness Kidron also said that companies adopting the rights as "best practices" would hopefully encourage others to do the same
Baroness Shields, Minister for Internet Safety and Security, said: "iRights gives a unique insight into how government can join with technology companies, civil society and business to make a better digital world for young people.
"We are using iRights in education, business and in our own services and digital communications."
Social media sites such as Twitter and Facebook allow users to delete their own posts, but images can still appear in search engines.
The report also led to the Children's Commissioner for England, Anne Longfield, announcing that she is launching a task force, Growing Up Digital, dedicated to improving the online lives of young people through the iRights framework.
She said: "If children of today and tomorrow are to grow up digitally, we need to be sure that the rights to protection and empowerment that they enjoy in their lives, are embedded in the new digital world they inhabit.
"As the legal guardian of children's rights and best interests in England, this is of uppermost concern to me as Children's Commissioner.
"I am grateful to iRights for the groundbreaGraking work they have undertaken in this fast developing area. I intend to build on this work to establish a new Growing Up Digital taskforce, which will launch in the autumn."