The regulator said it had agreed the £3 million package with E.On after it was found to have breached its reporting obligations under the Government's Carbon Emissions Reduction Target (Cert) programme.
E.On's £2.5 million payment will mean around 18,500 extra customers who are eligible to receive Warm Home Discount Broader Group payments will receive £135 to help with their 2013/14 winter bills.
The remaining £500,000 will be paid as a fine and "reflects the serious nature of inaccurate reporting", Ofgem said.
Under the Government's Cert programme, large energy suppliers were required to deliver efficiency measures to consumers and were able to distribute free energy-saving light bulbs to help achieve this.
However, Ofgem's investigation found that the reported distribution figure of around 3.4 million light bulbs was inaccurate, including some that went on sale in the Republic of Ireland rather than being distributed for free in Britain.
Ofgem's senior partner in charge of enforcement, Sarah Harrison, said: "This case leaves companies in no doubt that Ofgem takes reporting failures seriously. Accurate company reporting is essential to Ofgem's effective administration of the Government's environmental schemes. This settlement means that £2.5 million of additional help will go to some of E.On's most vulnerable customers. The settlement reflects E.On's co-operation with Ofgem's investigation, as well as the company's willingness to make up its shortfall for the Cert scheme. Without E.On's constructive engagement, the level of fine would have been much higher."
E.On chief executive Tony Cocker said: "We're sorry that these mistakes were made in 2010 and Ofgem has received a board level assurance that the necessary changes have been made. Our controls should have been stronger and our processes more robust.
"It was important to us that, as part of putting this right, customers in fuel poverty or in a fuel poverty at-risk group should receive a portion of the penalty we faced in the form of the additional payments we are making. We're pleased that Ofgem agreed and has allowed us to do so. Overall energy efficiency obligations have been met, with the shortfall being made up by additional measures. No consumers were misled because of this mistake but this does not take away from the fact it was an error that should not have been made."