The ban comes after 1,100 responses to a consultation which strongly supported introducing an age restriction on the drinks, external.
The new rules will come in via secondary legislation using powers from the Food Safety Act 1990.
Too much caffeine can cause a rapid heart rate, abnormal heart rhythms and seizures.
Although rare, there have been some deaths linked to excess caffeine.
The sugary versions of the drinks can also contribute to obesity and damage teeth, according to The Association of UK Dieticians.
Currently any drink, other than tea or coffee, with over 150mg requires a label warning of its high caffeine content that says it is not recommended for children or pregnant or breast-feeding women.
For most adults, up to 400mg of caffeine a day, or about four cups of instant coffee or five cups of tea, is safe.
Katharine Jenner, Executive Director of the Obesity Health Alliance, praised the policy and said restricting the sales of the drinks to children “at a vital time in their life is just common-sense”.
The British Soft Drinks Association said the ban was “unnecessary”.
A spokesperson said: “Since 2010, our members have committed not to market or promote the sale of energy drinks to under-16s, and all high-caffeine beverages carry a ‘not recommended for children’ label.”
The previous Conservative government had planned to introduce the ban, but scrapped the move in 2022, and said consumption should be a personal choice.
Northern Ireland, Scotland and Wales are also considering a ban.