The UK's largest retailer aims to cut the four billion plastic bags it dishes out annually by 25% within two years, it said today.
Tesco will award Clubcard points to people who recycle old carriers or pack up their shopping in other bags.
The chain has opted not to follow the example of Swedish firm Ikea by charging customers for new bags.
Instead it will give its 13 million Clubcard holders one point for every bag they don't take from stores.
Points will be awarded to shoppers who re-use old plastic bags - even those from rival chains - or bring other bags into store.
The Clubcard points will be redeemed as usual. They are worth 1p each or up to four times that amount if used for special deals.
Clubcard holders will also get one voucher each to redeem against a durable "bag for life" in Tesco stores.
Tesco chief executive Sir Terry Leahy said the chain had been working on ways to reduce carrier bag use.
"The results of our research tell us that we have to move the emphasis away from trying to force change and onto rewarding positive behaviour. In other words a more carrot than stick approach," he said.
All Tesco carrier bags will be degradable by the end of next month. The chain has brought in bigger, thicker bags in some stores so people use less.
Check-out staff will use their discretion in deciding how many Clubcard points to give out.
A host of TV stars will appear in adverts to mark the scheme's launch on August 14.
Local Environmental Quality Minister Ben Bradshaw welcomed the scheme, saying: "I strongly support moves to reduce the number of new plastic bags in circulation.
"Research shows that the most environmentally friendly thing to do is to get maximum use out of bags, whatever their material, and then recycle them."
Asda last night unveiled plans to introduce reusable 'bags for life' in its stores on August 14.
Priced at 5p, 1p of which will go to charity, the bags will be replaced free of charge by Asda when necessary.
The European Commission is set to impose a 10-15 per cent import tax on plastic bags imported from Thailand and China.
The duties, expected to get final approval at the end of this month, aim to correct imbalances in the market.
The British Retail Consortium said the tax would cost the UK an estimated £50 million in extra import duties.
Friends of the Earth supermarket campaigner Sandra Bell was unimpressed by the Tesco scheme.
"This is typical of the greenwash that Tesco has been churning out over recent months," she said.
"Even if it meets its target to reduce the number of bags being used, Tesco will still be handing out three billion plastic bags a year.
"And this is just a drop in the ocean compared to the mountains of packaging waste the chain creates."Reuse content