TSB chief executive Peter Pester told the Sunday Telegraph that TSB will begin its roadshow relatively soon, with the listing planned for the middle of next year.
The share sale will also include a retail offering, Mr Pester said.
Lloyds was ordered to sell the branches by European regulators as a penalty for receiving a £20bn taxpayer bailout in the 2008 financial crisis.
TSB has 4.7 million retail customers and 127,000 small business customers.
Mr Pester said: “It’s amazing hearing them talk about wanting a transparent bank.
“What they don’t talk about, interestingly, is a bank that pays them a bit more interest; what they say is ‘I want a bank that I know where my money is going’.
“There’s a sense with customers that they save in their local high street bank, and somehow that got distorted into the financial crisis with guys in the City making tens of millions and blowing the economy up.
“Customers now have a choice – they can allow their savings to be used to fund investment banking, to fund derivatives trading, to fund overseas speculation, to fund bankers’ bonuses, or they can come to TSB.”
Mr Pester said that in the ten weeks since TSB launched a new advertising campaign, customers had been signing up for current accounts twice as quickly as the group had estimated.
He compared the TSB offering to Fairtrade coffee.
Mr Pester said: “Literally every week we are seeing several thousand more customers join us than we would ever have expected.
“At this stage we are not seeing a particularly skew to any one bank; it’s coming from across the big four, but the smaller banks as well.
“I think we’re certainly rumbling our competitors. Not just because we’re taking big chunks of their customers, but I wouldn’t be surprised if we didn’t see the other big banks trying to claim this space of being a local bank, or a community bank.”
Mr Pester is preparing for the initial public offering next year and will hit the road soon with chief financial officer Darren Pope to meet potential investors, “explaining to them our local banking model, our clean balance sheet, the fact that we have none of the hangovers of the past, and explaining why this is a unique investment opportunity”.
He added: “It is the only bank share that you can buy that has just exposure to UK retail banking and nothing else.”