The UK's largest supermarket chain is the latest retailer to announce it is no longer going to accept personal cheques from customers.
Cheques account for just 4% of retail transactions
Tesco said the ban on cheques would take effect in all of its 2,000 stores from 25 February.
The company said customers would benefit from improved security and quicker service as a result.
The move follows similar announcements from Marks and Spencer and a range of other High Street retailers.
Tesco had previously banned cheques in a small number of its stores to test customer reaction.
It said all stores would display prominent notices to warn customers of the forthcoming change.
"Phasing out the use of cheques in stores will result in quicker service and improved security for our customers," said a spokesman for the retailer.
However, it acknowledged that the move might not be universally popular.
"We recognise that some people - especially the elderly - might be worried by this change, and this is why we have given customers plenty of notice," added the spokesman.
The supermarket said it would brief staff to advise older customers about alternative payment options.
Marks and Spencer (M&S) has said that it will no longer accept cheques in any of its stores from 1 March.
"Cheques now account for less than 2% of all transactions at M&S and that figure is declining year on year," said a spokeswoman.
Customers would still be able to pay their Marks and Spencer "&More" credit card bills by cheque in store, she added, but they would no longer be able to do so at the till.
Cardholders would have to use special deposit boxes located in store instead, she said.
Tesco and Marks and Spencer join a long list of retailers who have already stopped accepting cheques, including Asda, Argos, Boots, Debenhams, Next, Sainsbury's and WH Smith.
UK CHEQUE VOLUMES
2006: 1778 million
2005: 1931 million
2004: 2088 million
2003: 2251 million
2002: 2394 million
2001: 2567 million
2000: 2702 million
1999: 2859 million
1998: 2988 million
1997: 3091 million
Almost all the companies cited the declining popularity of cheque usage, a trend borne out by the statistics produced by the UK's payment association Apacs.
It said just under 5 million business and personal cheques were issued each day in 2006, compared with 11 million in the peak year for cheque volumes, 1990.
Only 4% of retail spending is still paid by cheque, compared with more than 60% by debit or credit card, it added. Cheque usage is expected to fall further in the next few years.
"Over the last year or so we've started to see a growing number of retailers who have decided not to accept cheques, so we are definitely starting to see the death of the cheque on the High Street," said Apacs' Jemma Smith.
"This is a trend that is undoubtedly in response to the fact that so few shoppers now want or expect to pay by cheque, because no retailer would be wanting to take this step if they thought they would lose business," she added.
However, she acknowledged that cheques remained vital for some transactions, such as sending money for someone's birthday or paying a credit card bill. For that reason, she said, she expected cheques would continue to be offered for some time yet.