Its new range includes a market-leading two year fixed-rate mortgage at 1.99pc, down from 2.64pc previously, although borrowers need a hefty 40pc deposit to take out the deal.
Tesco has also dropped the rate on another a two-year fix from 2.79pc to 2.39pc for borrowers with a 30pc deposit and said it was able to make the rate cuts due to its plans to use a Government scheme to kick-start lending by offering banks access to cheap funding.
Both the Tesco deals also carry fees of £995 and are available to customers who are remortgaging or buying a new home.
Rachel Springall, spokeswoman for comparison website Moneyfacts, said the last time a similar fixed deal was offered at 1.99pc was around a year ago.
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She said: "It's great to see Tesco Bank offering some attractive rates, especially breaking the 2pc barrier.
"The new two-year fixed deal from Tesco Bank will become the market leader at 1.99pc with a £995 fee and will require a 40pc deposit. In addition the two-year 2.39pc deal with a £995 fee will be the lowest rate for 30pc deposits.
"Customers will be able to acquire Clubcard points on each monthly repayment, where they can redeem them as vouchers to use in Tesco stores."
The supermarket giant only launched into the mortgage market in August, and offers loans-to-value (LTVs) at up to 80pc, alongside a range of banking and insurance products, with plans to launch cash Isas before the next tax year starts.
Mortgage availability has generally increased since the Bank of England and the Treasury launched the £80 billion funding for lending scheme at the start of August, although many headline-grabbing rates have been concentrated around people with larger deposits and have also come with significant fees.
Lenders have also toughened their borrowing criteria, meaning people have higher hurdles to jump to take out a mortgage.
The Council of Mortgage Lenders said yesterday that mortgage lending was 10pc down in September compared with the previous month, which appeared to reflect a drop in the number of people looking to buy homes, while remortgaging levels also remain weak.
The Bank of England has suggested it could be towards the end of the year before the effects of recent improvements to lenders' ranges show up in any mortgage lending figures, due to the typical lag of two to four months between mortgage approvals and sales taking place.
Benny Higgins, chief executive of Tesco Bank, said: "We are committed to responsible lending and hope to enable our customers to borrow a further £1 billion, over the next year, at affordable rates."