The firm's market value has slumped in the past year
Spanish bank Santander has agreed a deal to buy UK lender Alliance & Leicester (A&L) for about £1.26bn.
Santander said A&L shareholders would get one of its shares for every three they now hold in the UK bank.
Shares in A&L soared by more than 50% on Monday after it disclosed that it had received a bid approach, which the BBC revealed was from Santander.
Santander is effectively offering 317 pence per A&L share and expects the deal to be completed by October.
But BBC business editor Robert Peston says the deal with Abbey-owner Santander may pose competition issues.
Santander plans to merge A&L with Abbey, which it bought in 2004, leading unions to express fears about job losses.
But our correspondent added that the deal also represented an apparent vote of confidence in the UK's troubled housing market.
"The takeover - if successful - would be a great relief to the City watchdog, the Financial Services Authority - because it believes big banks are more robust in these uncertain times," he said.
"However, Alliance & Leicester has been a source of important competition in the UK's relatively concentrated banking market," he added.
"So there will be some concern that the disappearance of A&L as an independent entity would leave too much power in the hands of the big banks."
David Cumming, head of UK equities at Standard Life Investments, described it as "a gorgeous deal" for Santander, saying the bank was acquiring Alliance & Leicester "on giveaway terms".
"Given the potential integration benefits, other banks must surely be reviewing their options. I would be amazed if no one else counters with a higher offer in the next few months."
Banking analyst Ralph Silva on the deal
A&L is recommending the bid to its shareholders, who will have to approve the transaction before it can go ahead.
Like other British lenders, A&L has seen its share price slump due to the credit crunch.
Alliance saw its annual profits fall 30% last year amid turbulence in credit markets, which has forced it to write down the value of mortgage-backed investments by nearly £400m.
But unlike other leading UK banks, it has not had to tap its shareholders for additional cash to shore up its balance sheet.
Yet, A&L said the current tough economic climate made the deal even more attractive.
"A&L is a strong and attractive business and its resilient performance is proof of the quality of its franchise," said its acting chairman Roy Brown.
"However, the board is acutely aware of the significant external risks presented by the deterioration in economic conditions and the continuing turbulence in the financial markets."
Like other lenders, Alliance has reacted to the credit turmoil by reducing the number of mortgages it sells and pushing up the interest rates.
The proposed deal would boost Santander's presence in the UK, the Spanish bank said.
"We are very pleased to be working with the management and employees of A&L as we seek to build with Abbey one of the leading franchises in the UK banking sector," said its chairman Emilio Botin.
A likely tie-up between A&L and Abbey has got unions worried
But unions said they were worried about the implications of the deal for jobs at A&L's 700 or so High Street branches.
The Leicester-based business employs about 8,000 staff.
"Staff at A&L deserve to have answers about their future and we urge the company to be upfront about their intentions," said Andy Kerr, deputy general secretary of the Communication Workers Union.
At close, Alliance's shares were up 53% at 335.25 pence.
Shares in other lenders soared on the news, with Bradford and Bingley shares rising by more than 25% at one point before closing 11% ahead.