The pilot deal follows the partnership between British Gas, the Nectar loyalty scheme and Sainsbury’s revealed earlier this year.
Tesco and E.on will also add 50% of the value of Clubcard vouchers used to pay for E.on’s services so for every £10 voucher, customers can redeem £15.
E.on hopes the initiative will improve loyalty and boost customer retention.
The trial will run until 5 August 2011 and could be rolled out permanently.
The reward offer extends E.on and Tesco’s existing deal that allows customers to earn Clubcard points on their energy bills.