Social media firms will be required to delete information on children and adults when asked under new laws aimed at giving people a greater "right to be forgotten" online.
The Data Protection Bill will make it simpler for people to control how companies use their personal details, with extra powers for the information watchdog to issue fines of up to £17 million.
The new powers will mean people can ask social media platforms to delete information they posted in their childhood.
The bill will also require people to give explicit consent for their information to be collected online, rather than firms relying on pre-selected tick boxes.
The legislation will:
:: Allow people to ask for their personal data held by companies to be erased.
:: Enable parents and guardians to give consent for their child's data to be used.
:: Expand the definition of personal data to include IP addresses, internet cookies and DNA;
:: Make it easier and free for individuals to require an organisation reveal the personal data it holds on them.
:: Create new criminal offences to deter organisations from intentionally or recklessly creating situations where someone could be identified from anonymised data.
The legislation will bring the European Union's General Data Protection Regulation (GDPR) into domestic law, helping Britain prepare for Brexit because it will mean the systems are aligned when the UK leaves the bloc.
The Information Commissioner's Office will be given significantly tougher powers, with the maximum fine it can levy being increased from £0.5m to £17 million, or 4% of a firm's global turnover.
The bill, which was announced in the Queen's Speech, will be introduced in Parliament when MPs and peers return from the summer break in September.
Digital Minister Matt Hancock said: "Our measures are designed to support businesses in their use of data, and give consumers the confidence that their data is protected and those who misuse it will be held to account.
"The new Data Protection Bill will give us one of the most robust, yet dynamic, set of data laws in the world.
"It will give people more control over their data, require more consent for its use, and prepare Britain for Brexit.
"We have some of the best data science in the world and this new law will help it to thrive."
Information Commissioner Elizabeth Denham said: "We are pleased the Government recognises the importance of data protection, its central role in increasing trust and confidence in the digital economy and the benefits the enhanced protections will bring to the public."
Julian David, chief executive of industry body techUK, said implementing the GDPR regulations in full "puts the UK in a strong position to secure unhindered data flows once it has left the EU, and gives businesses the clarity they need about their new obligations".
Shadow culture secretary Tom Watson said: "Labour's manifesto committed to allowing young people to remove content shared on the internet before they turned 18, so we're glad the Government is taking action on this.
"As we are leaving the EU it is more important than ever that we have a robust data protection framework fit for the future.
"We'll be scrutinising the bill carefully to make sure it creates that future proof framework."