"We must do all we can to help children lead a healthy life," public health minister Jane Ellison said. (Agencies)
E-cigarettes, popular with teenagers, deliver a hit of addictive nicotine and emit water vapour to mimic the feeling and look of smoking.
The battery-powered devices can currently be bought online and in some pubs, chemists and newsagents.
The vapour is considered potentially less harmful than cigarette smoke and is free of some its damaging substances such as tar.
"We do not yet know the harm that e-cigarettes can cause to adults let alone to children, but we do know they are not risk free," Prof Dame Sally Davies, England's chief medical officer, was quoted as saying by the BBC.
Katherine Devlin, president of the Electronic Cigarette Industry Trade Association, welcomed the changes in the law, saying they had been asking for it "for years".
"It's high time that it was mandated in law so that it can be robustly enforced," she added, pointing out that product labelling made it clear e-cigarettes were not for under-18s.
Ministers also plan to make it illegal for adults to buy traditional cigarettes for anyone under 18, the report said.
They want to crack down on the number of young people smoking by bringing the law in line with restrictions on the sale of alcohol.
The new rules could be in force by the autumn and may mean anyone caught buying cigarettes for a child could be given a 50-pound fixed penalty notice or a fine of up to 2,500 pounds, the report said.
Some 41 per cent of 15-year-olds who smoke say they usually buy their cigarettes from someone else, rather than from a shop, according to Department of Health figures.
"That's why this measure is designed to help protect children from the dangers of being bought cigarettes by irresponsible adults - something that I hope concerned parents and responsible retailers will welcome," Ellison said.
The UK currently has few restrictions on the use of e- cigarettes, despite moves in some countries to ban them.
The law change for England will be introduced in Parliament this week as an amendment to the Children and Families Bill.
From 2016, the Medicines and Healthcare Products Regulatory Agency is expected to license e-cigarettes as a medicine in the UK.
Smoking remains one of the biggest causes of death and illness in the UK with around 100,000 people dying each year from illnesses linked to the habit.
"We must do all we can to help children lead a healthy life," public health minister Jane Ellison said.