Lloyds' subsidiary Halifax will pay a purchase price of around 3.8 billion pounds, representing a 2.5% premium on the gross book value and will be funded using existing internal resources, the lender said.
Britain's biggest supermarket chain Tesco plc said in May this year its banking unit would cease mortgage lending, citing cut-throat competition that has squeezed profits for lenders across the sector.
Uncertainty over Britain's exit from the European Union has prevented interest rate increases that could have boosted loan margins, while a glut of new banks and rules pushing established players to lend more have increased the supply of mortgages.
"The sale is in line with Tesco Bank's strategy of focusing on a reduced number of products and services that serve the broad range of Tesco customers, and will reduce operating and funding costs," the supermarket said in a statement on Tuesday.
Under the ownership of Tesco Bank, the portfolio, which comprises over 23,000 mortgage customers, generated income of around 81 million pounds and a pre-tax profit of around 9 million pounds in the year to February 28.
The ownership of the portfolio is expected to transfer at end of September, with transfer of the legal title anticipated by end of March 2020.
It will add to Lloyds' already hefty mortgage portfolio and consolidate its position as the biggest mortgage lender in the UK; its lending stood at 42.5 billion pounds at the end of 2018, according to UK Finance, the trade body for UK banking and financial services.