Chief executive Tony Cocker said changes announced by the Government earlier this week reduced the overall level of the rise that was necessary to cover extra costs.
The company said it was "working hard to limit the impact on its customers" by announcing a lower average percentage rise than any other major supplier.
It will see the average variable dual fuel bill go up by 3.7% or £48, electricity only prices go up by 3.7% or £20, and gas only climb by 4.6% or £37. The changes will take effect from January 18.
The increase is the last to be announced by any of the so-called Big Six firms that dominate the energy supply market.
British Gas customers were told they faced a 9.2% tariff hike, with SSE rates going up 8.2%, npower 10.4%, and Scottish Power 8.6%.
However, they have said they will pass on savings from a shake-up on green levies announced earlier this week that it is estimated could shave £50 off bills.
EDF has announced a 3.9% rise, saying it was holding back the full impact of rising costs in anticipation of the Government's changes.
It blamed the rising costs of delivering energy and buying wholesale gas and electricity while also admitting £4 on every typical bill would go on extra profit.
Mr Cocker said: "There is no escaping the simple fact that any price rise is unwelcome news for customers.
"We know that, which is why we have held off for longer than most of our competitors and worked hard to keep our rise as low as possible.
"We have moved quickly to pass on the benefits of changes announced by the Government at the beginning of this week.
"This means we have reduced the overall level of a rise that is necessary to cover the extra costs we are seeing in some areas, as well as making sure we continue to deliver a sustainable future for all of our employees and maintain our investment in the UK.
"Whilst there can be no guarantees, the likelihood of further price rises over the next 18 months caused by an increase in the cost of social and environmental obligations has receded due to the recent action taken by the Government."
Asked about the timing of the announcement, which came amid a media focus on the death of Nelson Mandela and the devastating storms across the country, Downing Street said: "It is for them to explain their decisions."
Caroline Flint, shadow energy and climate change secretary, said: "This latest price hike just goes to show that even after the Government's changes to green levies people's energy bills will be higher this winter than last. This is why nothing less than a price freeze and reforms to stop the energy companies overcharging again in the future will do.
"The Government boasts about the economic recovery, but soaring energy bills are one of the main reasons working people are £1,600 a year worse off under David Cameron."
An analysis of Big Six tariffs by Consumer Futures showed that following the latest changes, npower customers will face the largest bills, with the typical average charge paid by direct debit at £1,396.
Next is British Gas on £1,388, followed by Scottish Power on £1,383, SSE on £1,376, E.ON on £1,322 and EDF on £1,300.
However the table does not take into account pledges to reduce tariffs in the light of changes to green levies.
Audrey Gallacher, director of energy at Consumer Futures, said: "E.ON's price rise of 3.7% is unwelcome, but not surprising with this being the sixth price increase announcement in recent weeks.
"Rising prices, the complexity of the market and uncertainty on government policy has created a crisis of confidence in public trust.
"The energy marketplace needs urgent scrutiny, with a competition review to look at the structure of the market and a value for money review to ascertain the costs and benefits of government policy."
Energy Secretary Ed Davey said the E.ON rise was "disappointing" but added that the rise was lower than it would have been because of the changes announced by the Government.
He added: "This does not let energy companies off the hook. They will keep up their efforts to help people in fuel poverty cut their bills by making sure their homes leak less heat, and they will have to be more transparent about what they're spending on social and environmental measures."
© 2013 Press Association