Lloyds had previously indicated that it would sell up to half of the institution with strong Scottish roots in the first tranche. But analysts said the bank is coming to the market at a tough time.
Mr Pester said: "What we are bringing is a bank that is there to service local communities. It is a bank that is clean in the sense that we are not cursed with the sins of the past, which is very important."
UK banks have been forced to hand over billions of pounds in compensation for mis-selling products such as payment protection insurance.
But TSB has a conduct indemnity which means responsibility for past mis-selling rests with Lloyds.
The flotation comes a year after the collapse of the planned sale of the business, which has 4.5 million customers, to Co-operative Bank. It was revealed shortly afterwards that Co-op Bank had a large capital shortfall.
António Horta-Osório, chief executive of Lloyds, said "The decision to proceed with an initial public offering of TSB is an important further step for the group as we act to meet our commitments to the European Commission.
"TSB has a national network of branches, a strong balance sheet and significant economic protection against legacy issues."
Lloyds has to sell its holding in TSB by the end of 2015 as a condition of its £25 billion taxpayer bail-out five years ago.
The bank has 189 branches in Scotland out of 631 UK-wide, which is a 6 per cent share of the British banking network.
TSB has £23.3bn of customer deposits and £19.7bn of customer assets as well as the title to £3.3bn Lloyds mortgages.
The bank said yesterday it plans to grow its balance sheet by 40 per cent to 50 per cent over the next five years. Mr Pester said this would be achieved by boosting its 4.2 per cent share of the current account market and using the proceeds to sell home loans via the mortgage broker sector from which it is currently absent. He said that TSB had only to take a 3 per cent share of the broker market to reach its target growth.
TBS was launched as a standalone bank in September.
However, TSB can trace its roots back to the formation of the trustee savings bank movement in 1810 by the Reverend Henry Duncan in Dumfriesshire. Among TSB's assets is the Savings Banks Museum in Ruthwell.
But its headquarters are on the site of TSB's former London office.
Mr Pester said TSB would retain its branch network in Scotland.
"There are no plans to change branch numbers," he said. "When you contrast us with other Scottish banks, like RBS (Royal Bank of Scotland), they have 200 more branches than we do and they reach about 1% more of the Scottish population than we do."
The IPO will take place before the end of June. It is expected to value TSB below its book value of £1.5bn, meaning Lloyds will make a loss on the sale.
Michael Hewson, chief markets analyst at CMC Markets UK, said: "Unfortunately its timing could well be a little bit off if the lacklustre performance from Saga's IPO earlier this month is any guide. The initial valuation has been set at around £1.5bn but could well be less given that the appetite for IPOs appears to be showing some signs of waning."
TSB said it expects to pay a dividend for the 2017 financial year.
The retail shares are being sold through intermediaries in the manner of the Royal Mail flotation. A bonus of one share for every 20 bought will be awarded if the shares are held for a year.