The International Monetary Fund announced last night that it approved a three-year, $4.9 billion rescue package for Brazil which, coupled with new loan agreements with its private bankers, is designed to help that financially troubled Latin American nation stay afloat this year.

Last Friday, after two months of negotiations, Brazil's bankers agreed to lend it $4.4 billion in new money this year and to postpone $4 billion in loan repayments due in 1983.

The bankers also agreed to supply Brazil with up to $10 billion in financing to support its import and export activities and have come close to fulfilling the $7.5 billion the country says its banks need in short-term credit lines and deposits with other financial institutions.

Brazil owes more than $80 billion, perhaps now as much as $90 billion, to foreign governments and banks. Because of the worldwide recession and the sharp decline in world trade, the country is having difficulties paying its debts. Many other major developing nations, including Mexico--whose debts are about as big as Brazil's--and Argentina, have had to renegotiate their debts to private banks and turn to the IMF for assistance.

IMF officials said last night that the "banks have done extremely well" in two months of complex negotiations that involved at various points more than 600 institutions. For a while the negotiations stalled when many medium-sized U.S. banks as well as some large foreign banks cut back sharply on the money-market lines they extended to Brazilian banks.

Such big U.S. banks as Chase Manhattan and Bank of American regularly were pressed to increase their nightly loans to Brazilian banks to make up for the others.

But last week, big banks in Europe and Japan began to boost their money market credits to Brazil after their regulatory agencies stopped criticizing those loans. U.S. regional banks, however, appear to remain adamant in trying to reduce their money market exposure to Brazil.