Britain's largest retailer has been running a pilot banking service in Glasgow since 2006 and will next month launch three new branches in Bristol, Blackpool and Coventry.
The outlets will offer Tesco's existing personal finance products, which include credit cards, savings accounts and insurance, as well as terminals for accessing Tescocompare.com, the chain's online comparison service.
The company hopes to introduce its own range of current accounts within two years, depending on when it can organize the necessary IT infrastructure.
Last summer, Tesco bought out Royal Bank of Scotland's 50 per cent share in Tesco Personal Finance for around Â£1 billion ($1.4 billion).
Commenting on the plans, Tesco told the Financial Times it would be a "responsible lender" aimed at customers "looking for a more traditional bank".
Shore Capital analyst Clive Black said Tesco has "positioned itself extremely well for financial services" and the initiative could see Tesco Personal Finance triple its revenues over the next five years to Â£600 million.