Ian Clink, the chief executive, said customers will initially be able to check account balances and transfer money over the Internet. However, he expects the service to be extended to cover a wider range of products soon.
Mr Clink said the venture's link with Tesco gave it access to new customers at a lower cost than competitors who need to spend millions of pounds on subsidising rates and promoting their brands through advertising and direct mail.
The number of customers visiting Tesco's website each week has risen from 55,000 to 78,000 in the past few months. The company said its Internet- loans offer is one of the most popular pages on its website.
"We are not starting anything new. There are no large bills attached," Mr Clink said.
"Tesco has the clear ambition to be the number one Internet retailer in the world. You will see Tesco becoming a major player in the Internet and we will be part of that."
Tesco Personal Finance boasts more than 1 million customers at present, 350,000 of them with savings accounts. It aims is to raise that to 3 million customers in the next few years.
Tesco's move into banking had a huge impact when it was announced two years ago. But it is now the new entrants - led by Prudential with its direct banking brand Egg - which are creating the biggest splash.
Mr Clink said that unlike Egg and its imitators, which are losing large amounts of money, Tesco is not in the business of offering unsustainable rates as bait to hook in customers but is actually now in profit.
"We are one of the few institutions to have increased not just the number of customers but the size of their balances, despite the likes of Egg," Mr Clink said.