The information was revealed in the bank's stock market flotation prospectus, which was published yesterday.
As well as new branch openings, the expenses will also cover refurbishment and relocation, digital investment and spending on branding and customer service improvements.
Chief executive Paul Pester said: "We are delighted to confirm that we will bring TSB to more communities and high streets across Britain by investing in our branch network."
The bank said it was too early to say where in the UK the investment would be targeted, but 185 of its sites are in Scotland out of a network of 631.
The TSB shares will be priced between 220p and 290p, meaning that at the lower end the market capitalisation of the bank could be about £1.1 billion, with the higher figure valuing it at £1.45bn.
Even the greater sum is less than the £1.5bn of book value, the net value of assets, attached to TSB, suggesting investor appetite for initial public offerings (IPO) may be cooling.
Owner Lloyds Banking Group has to sell the TSB by the end of 2015 to meet European Commission regulations on state aid. It previously agreed a £750m deal with Co-operative Bank but that transaction fell apart in April last year when the latter discovered a £1.5bn hole in its accounts.
The London market has been flooded with IPOs this year but there have been signs investor appetite is waning, with retailer Fat Face recently cancelling its flotation plans and a number of other businesses listing at the lower end of their valuations.
Ed Woolfitt, head of sales at stockbroker Galvan, said: "I am feeling these IPOs are starting to grow weary on investors. Bearing in mind Lloyds need to make the disposal as they are obliged, [the lower price] may be just a case of them making sure it is fully subscribed to."
Oriel Securities analyst Vivek Raja said the valuation reflected weak profitability at TSB, which could be explained by its loan book predominantly comprising mortgages from the Cheltenham & Gloucester building society, which are capped at two per cent over the base rate compared with a market average of 3.9 per cent.
TSB has about 4.5 million customers and six per cent of branches across the UK, which makes it the seventh largest retail bank.
It hopes to attract customers fed up with their current providers and has agreed a deal with its parent for indemnity from historical conduct-related losses such as mis-selling of payment protection insurance and other loans.
Jefferies analyst Jo Dickerson said: "It's going to be a very clean balance sheet, so if it comes at a discount to book one would think that's going to be very attractive."
The final pricing for TSB is to be confirmed on June 20, with conditional dealing in the shares to begin on the same day.
The bank has already said it does not expect to be paying a dividend until at least 2017 and hopes to expand its balance sheet by up to 50 per cent over the next five years.
It wants to grow its shares of the current account market from 4.2 per cent to more than six per cent, as well as opening up its mortgage products to brokers by the end of next year. At the end of 2013, Scottish customers accounted for about 24.1 per cent of its £17.7 billion mortgage book.
The prospectus noted Scottish independence, rising house prices and a rise in interest rates as among the risks facing the bank. Underlying TSB profits for 2013 were put at £82 million.
Mr Pester will receive an annual salary, pension and benefits worth £877,500 and could be paid up to £1.68 million if targets are hit.