The International Monetary Fund last night gave formal approval to a loan of $3.9 billion to Great Britain over the next 24 months, conditioned on an austerity program announced last month by the British authorities.

Britain can draw $1.16 million immediately. But not more than a total of $2.26 billion in the first 12 months.

The arrangements calls for Britain to observe various "performance clauses related to the program for strenghtening the United Kingdom's economy," the IMF said.

Before Jan. 16, 1978 - or before the final $1.64 billion of the loan can be drawn - another review of the progress of the British economy will be conducted, the IMF said.

The British government, in a "letter of intent" to the IMF on Dec. 15, spelled out a comprehensive program of spending cuts and borrowing reductions designed to restore a degree of confidence in the pound. This followed weeks of analysis of the British economy by a special IMF team.

It was also announced yesterday that to provide enough resources for the loan to Great Britain, nine countries would put up $3.3 billion in their own currencies, supplementing what is already on hand in the IMF.

Eight of these countries are participants in the so-called General Arrangements to Borrwo (GAB), a group of IMF nations that provides main support for the agency. The nations, and the amounts they will advance, are: the United States., $1.1 billion; West Germany, $910 million; Japan, $644 million; the Netherlands, $122 million; Canada, $64 million; France, $58 million; Belgium $52 million; Sweden, $23 million.

In addition, Switzerland, a non-IMF member, will loan $348 million to the fund.

Great Britain has other outstanding IMF loans, totaling $2.78 million.

In a brief review of the British economy and future prospects, the IMF noted that the recent government strategy of relying on exports and business investment as an impetus to growth had not produced the desired results.

In recent months, the IMF said, the improvement in price inflation had ended, and there are signs of new price rises. It expressed the hope that the new austerity program, buttressed by the $3.9 billion loan, will reverse those trends. There was also a muted warning that sustained voluntary cooperation by employers and trade unions is crucial to the success of the effort.