TSB chief executive Paul Pester says there is "strong appetite" from investors for the flotation of TSB, with optimism in the UK and overseas over the strength of Britain's economic recovery.
Further tranches of TSB will be floated later, with Lloyds obliged to dispose of its remaining interest in the business by the end of 2015.
Details of the pricing of next month's offer have yet to be announced but reports put the book value of TSB at about £1.5 billion.
TSB is protected against compensation claims by its parent company, the bank's chief executive Paul Pester says.
TSB boss says it has "indemnity" against any claims for misconduct (PPI etc) until it lists. Lloyds would deal with compensation.
Misconduct claims for the missale of payment protection insurance (PPI) have cost the industry billions of pounds, according to estimates from the Financial Conduct Authority.
Lloyds chief executive Antonio Horta-Osario says TSB has "a strong balance sheet" and is well protected from the issues that caused the banking crisis.
TSB has a national network of branches, a strong balance sheet and significant economic protection against legacy issues.
It is already operating on the UK high street and is proving to be a strong and effective challenger, further enhancing competition in the UK banking sector.
TSB will offer less than a quarter of its available shares to ordinary members of the public, its boss has said.
ITV News Business Editor Joel Hills reports:
TSB is to list next month. 25% stake in the bank will be sold. Boss says 15 - 20% of shares will go to small (retail) investors.
Paul Pester says TSB will not pay a dividend until 2017 at earliest as all profits will be channelled into growing bank.
Shares in TSB will be available to members of the public via intermediaries, as well as institutional investors.
Lloyds Banking Group said the retail offering will contain an incentive allowing each retail investor to receive one free share for every 20 shares acquired up to the value of £2,000 and kept for a year after the float.
A 25% stake in TSB is to be floated on the stock market next month, owner Lloyds Banking Group has announced.
Customers of banks including Lloyds, TSB and Halifax were left unable to withdraw cash, after two Lloyds Banking Group servers went down.Read the full story ›
A spokesperson for Lloyds Banking Group has said the IT problems encountered earlier are now resolved.
We apologise that earlier today, between 3pm and 6pm, some customers were unable to complete their debit card transactions. Although the majority of transactions were unaffected, we are very sorry for the inconvenience that this will have caused.
At the same time, some customers encountered problems at approximately half of our 7,000 ATMs. This was resolved by 7.30pm, and all of our ATMs are now working.
Online and telephone banking were unaffected by the problems.
The CEO of TSB has tweeted that the cause of the banking problems are now fixed but added that it will take a while to clear the backlog.
The cause of the problems at TSB is now fixed. It'll take a while to sort the backlog. Sorry customers may have problems for an hour or so
Thanks to all TSB colleagues who worked so hard this afternoon to fix the IT issues. Sorry once again to all our customers affected. PDP
A Lloyds Banking Group spokesperson has told ITV News that two out of seven of the banking group's servers have gone down, which has led to customers being unable to withdraw cash or use their debit cards.