Ofgem said correct billing was an essential part of customer service and large catch-up bills could leave consumers struggling financially or even in debt to their supplier.
The average back bill was £1,160 last year.
Customers have received bills in excess of £10,000 in extreme cases, according to Citizens Advice.
Back bills can result from problems with a supplier’s billing system or from suppliers estimating bills until they use an actual meter reading, which may show that the customer’s consumption was higher than expected.
Many suppliers are part of a voluntary agreement not to back bill customers past 12 months, but this does not include all companies and those that have signed up do not always stick to it, Ofgem said.
The ban will not apply to customers who actively prevent suppliers from taking or receiving accurate meter readings.
But consumers will not be at fault for failing to provide meter readings,and Ofgem said suppliers would need to assess consumer behaviour on a case-by-case basis.
The new rule will come into effect at the start of May for domestic consumers and in November for micro-businesses.
Rob Salter-Church, Ofgem’s interim senior partner for consumers and competition, said: “Getting billing right is an essential part of customer service and it’s unfair that consumers should be left out of pocket when, through no fault of their own, they’re issued with a shock bill from their supplier.
“So we’re taking action and banning suppliers from issuing back bills beyond 12 months where it’s not the customer’s fault.
“This sends a strong message to suppliers to improve the accuracy of the bills they send to their customers.”
Lawrence Slade, chief executive of Energy UK, said: “Energy companies take accurate billing very seriously and where there are problems, the majority are resolved within 24 hours. “Suppliers are actively working to improve billing for their customers. That is why companies covering 80 per cent of the market have signed up to the Energy UK Billing Code to ensure greater accuracy of bills. Audit results of the code show year-on-year improvement and complaint numbers are falling.”