The supermarket has taken out newspaper adverts apologising to customers.
It comes after thousands of motorists reported that they had broken down when their vehicles were filled with faulty fuel, which affected oxygen monitors.
Tesco says in the adverts that its petrol can now be bought "with confidence".
The advert says: "If petrol bought at Tesco has damaged your cars, we'd like to say how sorry we are. More to the point, we promise to pay for repairs."
The firm said checks traced the problem to a batch of unleaded fuel used by a supplier in Essex.