Both deals are available at 60% loan to value (LTV).
The lender said its new five-year mortgage at 1.68% with a £995 product fee was now the lowest on the market.
It also cut the rate on its two-year remortgage product at 60% LTV with no fee to 1.53%.
Both products will move onto the lender’s standard variable rate (currently 3.89%) at the end of the fixed-rate period and early repayment charges may apply.
Tesco Bank managing director David McCreadie said: “We are pleased to introduce our new market-leading five-year fixed rate product for customers who are looking to remortgage their home, helping them to make their money go that little bit further.”