Lloyds Banking Group is to sell 35 percent of its stake in TSB, up from the original 25 percent.
The decision has been taken as a result of heavy investor demand for the stock market listing.
The shares have been ten times oversubscribed.
Shares leapt 12 percent on their opening.
TSB is now valued at 1.6bn euros.
The sale is the result of a European ruling, which ordered Lloyds to sell 631 branches and all remaining shares in TSB by the end of 2015.
TSB has 4.5 million customers and is the seventh largest retail bank in the UK.