JPMorgan Chase is to buy Wall Street's fifth-largest investment bank, Bear Stearns, for $2 a share - a fraction of its previous value.
The news has rattled investors worldwide, who fear that the credit crisis is deepening.
The bank got into trouble over its sub-prime mortgage debts, and other banks had stopped lending to it.
The rescue has been backed by the US Federal Reserve, who will lend $30bn and lower its discount rate to 3.25%.
The discount rate is the rate at which the Fed lends to the banking sector, but the Fed is widely expected to slash interest rates that affect consumers as well - by up to 1% - when it meets on Tuesday.
Taking inflation into account this would take interest rates into negative territory.
And it has created a new lending facility for big investment banks, who will be able to borrow against the value of their mortgage assets.
Stock markets fell sharply around the world on Monday, with the Hong Kong index down 5%, the Japanese market nearly 4%, while London's FTSE dropped 100 points on its opening.
Credit crunch victim
MAIN SUB-PRIME LOSSES SO FAR
Merrill Lynch: $14.1bn
Morgan Stanley $9.4bn
Bear Stearns: $3.2bn
Deutsche Bank: $3.2bn
Bank of America: $3bn
Royal Bank of Scotland: $2.6bn
Freddie Mac: $2bn
JP Morgan Chase: $3.2bn
Credit Suisse: $1bn
Source: Company reports
The deal values Bear Stearns, which has been at the centre of the US mortgage debt crisis, at just $236m (£116m).
Its shares have lost 98% of their value since their high of $158 in April one year ago, when the bank was worth $18bn.
It means that the former chief executive of the bank, Jimmy Cayne, the richest boss on Wall Street, has seen his fortune plummet from $1bn to $12m.
In October, the shares were still worth $117, but by Friday, they had fallen to $30 (£15) after an emergency rescue package was announced.
Under the deal, which emerged on Sunday, the Federal Reserve will fund up to $30bn of Bear Stearns's less liquid assets.
In turn, JP Morgan will guarantee to meet all the payments due to Bear Stearns clients.
The fear was that the collapse of one of the biggest names on Wall Street could have sent shock waves throughout the entire financial system.
Bear Stearns's problems stem from the global credit crunch and the worry is that other lenders may also have major funding problems.
Last week, speculation had intensified that the bank was struggling to fund its daily business.
BBC business editor Robert Peston said Bear Stearns was taken to the brink of insolvency last week by a sudden collapse in confidence on the part of its hedge fund clients.
As a result, these clients rushed to withdraw their assets.
The credit crunch was caused because banks became less willing to lend to each other after they suffered large losses on investments linked to the US housing market, and the sub-prime sector in particular.
But the crisis has now become more general, with other kinds of assets also looking vulnerable.
Sub-prime lenders focus on clients with poor or non-existent credit histories, and a record number of borrowers have defaulted on loans.
The subsequent freezing-up of the credit markets created problems for a number of companies which relied on borrowing money to fund their business.
In the UK, Northern Rock ran into trouble when its line of relatively cheap credit dried up.
At the end of last year, Bear Stearns reported that it had made its first ever quarterly loss after buying investments linked to the US mortgage market.
It was one of the first to admit it had problems linked to sub-prime mortgages, after two of its hedge funds had to be bailed out in July.
Robert Peston said that last week's move by JPMorgan and the Fed of New York was essentially a central bank bailout, and described the crisis as "America's Northern Rock".