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The landmark all-share deal, effectively a rescue plan for Britain's biggest mortgage lender, comes after HBOS shares plummeted in recent trading following days of global economic crisis.
Lloyds TBS will pay wholly in shares.
Together, the banks hold nearly a third of Britain's savings and mortgage market but competition watchdogs will reportedly not block the deal as it was backed by the government.
Sir Victor Blank, chairman of Lloyds TSB, said the deal offered a "good deal for customers and shareholders" while his HBOS counterpart Dennis Stevenson said it was "the right transaction for HBOS".
HBOS shares were down 19.2 percent at the close of trading on Wednesday, against the backdrop of the dramatic collapse of US investment bank Lehman Brothers, nationalization of U.S. insurance giant AIG, and shock after shock in financial markets.
Heavy losses earlier on Wednesday prompted the Financial Services Authority (FSA) to issue a statement saying HBOS was well-funded, in an attempt to avoid a flood of savers trying to withdraw their money.
Prior to the reports of the takeover talks, HBOS shares had nosedived 52 percent to a low of 88 pence, as investors took fright at the state of the global banking sector despite news of the rescue for AIG, which was on the verge of bankruptcy.
News of takeover talks for HBOS had helped push the banks stock back into the black, at one point rising to 220 pence.
But at the close of trading, HBOS was down 19.2 percent at 147.1 pence, its third day running of heavy losses. Lloyds TSB shares were unchanged at 279.75 pence.
The deal values HBOS shares at 232p each, significantly more than Wednesday's closing price of 147.1p, the BBC said.
Under the deal, HBOS shareholders will receive 0.83 Lloyds TSB shares for every HBOS share.
Lloyds TSB shareholders will own approximately 56 per cent of the issued share capital under the acquisition and existing HBOS shareholders approximately 44 per cent.
Chancellor of the Exchequer Alistair Darling said Wednesday the British government was doing "everything possible at this time... that we help homeowners, we help savers by maintaining the stability of the banking system."
The value of shares in HBOS -- created by the merger of Bank of Scotland and Halifax in 2001 -- had slumped by a total of 36 percent over the course of Monday and Tuesday.
It has 258 billion pounds of savings and the strongest capital ratio, the most common measure of bank strength, of its domestic rivals.
London's FTSE 100 index saw a turbulent day of trading Wednesday, with much activity driven by concerns over HBOS's situation, closing down 2.25 percent at 4,912.40 points.