The proposals, which would only be put in law if the Tories win in May, would shut down any website refusing to follow the rules.
Culture Secretary Sajid Javid said it was about protecting children from inappropriate content.
He said an independent regulator would be set up to police the new rules.
Last week a Childline poll found nearly one in ten 12 -13 year olds are worried they are addicted to pornography.
Mr Javid said: "If you want to buy a hard-core pornography DVD in a store you need to prove your age to the retailers.
"With the shift to online, children can access adult content on websites without restriction, intentionally or otherwise.
"As a father to four young children, I worry, like every other parent, how easy it is for them to view explicit material.
"That is why we need effective controls online that apply to UK and overseas.
"This is about giving children the best start in life; we do not want to prevent adults from accessing legal content but we do want to protect our children from harmful material, so they are free to develop a healthy attitude to sex and relationships."
The Mothers' Union has welcomed the proposal after chief executive Reg Bailey was commissioned by the government to investigate the sexualisation of childhood.
He said: "A key recommendation of the Letting Children Be Children review ... was to help parents protect children from inappropriate content on the internet especially pornography.
"Although huge progress has been made, this is a real step forward.
"Whilst I do not underestimate the energy that will be needed to implement this effectively, I am greatly encouraged by the Prime Minister's continuing personal commitment to this task."
Speaking to the BBC Mr Javid said the plans could mean anyone wishing to view pornography would have to have a credit card to prove they are over 18.