The temporary price cap, which comes into effect in April, was one of the measures recommended by the Competition and Market Authority after its two-year investigation of the energy market, the BBC reports.
The levels of the cap vary for gas and electricity by meter type and region.
It will be updated every six months and is expected to stay until 2020.
That is when the roll-out of smart meters is set to be completed, which will benefit prepayment customers who have a smaller choice of tariffs available to them.
Ofgem chief executive Dermot Nolan said: “We want all consumers to enjoy the benefits of a more competitive energy market, regardless of their circumstances.
“Customers who prepay for their energy are denied the best deals on the market available to those using other payment methods.
“They are also more likely to be in vulnerable circumstances, including fuel poverty. This temporary cap will protect these households as we work to deliver a more competitive, fairer and smarter market for all consumers.”
Gillian Guy, chief executive of Citizens Advice, welcomed the news and said: “This cap should stop some of the poorest households paying over the odds to heat and light their homes.
“It will help millions save money but action shouldn’t stop there.
“The government has rightly expressed concern that loyal customers on standard tariffs are paying over the odds for their gas and electricity.
“It could help more struggling households, including low-income pensioners and families, by extending this cap to people eligible to receive the Warm Homes Discount.”
At the end of December 2015, there were four-and-a-half million prepayment electricity accounts and three-and-a-half million gas accounts – representing 17 per cent and 15 per cent respectively of all accounts in the UK.