The agreement, which would have seen 23 per cent of the company pass into the US group's control, was broken after it emerged that B&B was to have its rating downgraded for a second time by Moody's.
This meant that TPG could use a clause in its contract, which allows the firm to walk away if these separate reductions occurred.
A consortium of four firms has now agreed to inject $800 million of capital into B&B, in lieu of the TPG deal.
The bank is also planning a $500 million rights issue - which chairman Rod Kent said would still go ahead despite the rapid recent erosion of B&B's stock.
"B&B continues to be well-funded and the capital raising will reinforce our position as one of the better capitalised banks and one of the leading mortgage and savings banks in the UK," he said.
As markets reacted to the TPG news, B&B shares were down seven per cent in London trading this morning.
The stock has lost 90 per cent of its value since the beginning of 2008.