The offer comes with a sweetener for ordinary retail investors with the pledge that they will receive one free share for every 20 they hold on to for a year - up to the value of £2,000.
Lloyds is selling about a quarter of the business, with up to a fifth of this chunk expected to be sold to retail investors and the rest likely to be snapped up by City institutions. A prospectus for the sale will be published in mid-June.
TSB, famous for its 1980s slogan “the bank that likes to say yes”, traces its history back more than 200 years. It was floated in 1986 and merged with Lloyds in 1995.
A taxpayer rescue of the group during the financial crisis - following which the Treasury still owns a 25 per cent stake in Lloyds - meant that it was obliged to spin off hundreds of branches under EU rules on state aid.
The collapse of a deal to sell them to the Co-op saw the revival of the TSB brand, which re-launched last September with former Virgin Money boss Paul Pester at the helm, and which is splitting off to become a new “challenger bank” to larger rivals.
With 4.5 million customers and 631 branches, it is the seventh largest high street bank in the UK and the chief executive said it plans to expand its balance sheet by half as it expands mortgage lending and extends its share of the current account market.
But Mr Pester warned there would be no “significant dividend” until 2017.
Details of the pricing of next month’s offer have yet to be announced but reports put the book value of TSB at about £1.5bn.
The announcement comes at an uncertain time for stock market flotations, with fashion retailer FatFace abandoning a shares offer and over-50s holidays-to-insurance group Saga selling stock at the bottom end of an expected price range.
But Mr Pester said there was a “strong appetite” from investors for the TSB offer, with optimism from the UK and overseas over the strength of Britain’s economic recovery. He expected 15 per cent to 20 per cent of the shares in the float to go to retail investors.
Further tranches will be sold off later as Lloyds must dispose of its holdings in the business by the end of next year.
Its attractions include being free from scandals of past years which have continued to haunt rival banks, such as the payment protection insurance (PPI) mis-selling affair which has cost billions in compensation and whose shadow still hangs over lenders.
TSB will be protected from the legacy by Lloyds, which will be liable for any claims up to the date of next month’s float, and Mr Pester said the revived bank had no intention of repeating the mistakes of the past.
“We have no intention at all of creating the conduct tail that other banks have suffered from,” he said.
Georgina Mitchell, head of investment services at Leeds-based Redmayne-Bentley, said yesterday: “With only a hand full of initial public offerings open to retail investors over the last 12 months, today’s announcement represents a great opportunity to purchase shares in a well-known, high street bank. IPOs are very much the talk of the stock market at the moment, so we will look forward to working with Lloyds in what we expect to be a highly sought after offering.”