E.ON has been a Clubcard partner for 13 years, previously allowing customers to earn Clubcard points on money spent on energy bills.
Under the terms of the enhanced scheme, 50% will be added to the value of the vouchers, meaning £10-worth Clubcard points can be used to pay £15 of an energy bill. However, the deal currently excludes E.ON's StayWarm, WarmAssist and Age UK tariffs, as well as customers using pre-pay meters.
The initiative, which E.ON claims is the first of its kind in the energy sector, will be trialled until 5 August, with a view to extending it if both brands consider it successful.
The deal will be promoted through Tesco's monthly Clubcard statement mailer, as well email and online activity. E.ON will also look to raise awareness through a direct mail push.
"Customers tell us that money is tight so being able to offer them a new way to save money on energy bills is really important. These kinds of rewards on energy just aren't available elsewhere on the market," said Janet Smith, director of Tesco Clubcard.
E.ON marketing director Jeremy Davies added: "Many of our customers are struggling to pay their bills, and want to be rewarded for their loyalty to the brand. We're seeking to help customers manage bills, including new ways to pay them."
Earlier this year, British Gas joined the Nectar loyalty scheme, replacing EDF Energy, and has partnered with Sainsbury's to offer a range of services.