Chief executive Tony Cocker said changes announced by the Government this week reduced the level of the rise 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 a year, 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.
Elizabeth Gore, deputy director of fuel poverty charity Energy Action Scotland, said: "Just one day after learning from the Government that they would get a £50 cut in their energy bills, households are given the news that yet another energy company is increasing its prices.
"Customers are no doubt thinking that it is a case of giving with the right and taking with the left."
British Gas customers were told they faced a 9.2% tariff hike, while rates from SSE are going up 8.2%, ScottishPower by 8.6% and npower by 10.4%.
However, they have said they will pass on savings from the shake-up on green levies announced this week.
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.
While E.ON's rise is lower than those of its rivals, it is still higher than the inflation rate of 2.2%.
The firm 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.