Mr Camdessus said his departure was for personal reasons, but there has been criticism of the role the organisation played in the Asian debt crisis last year. He is said to have been discussing taking a job with the Vatican Bank when he leaves in February.
In a letter to the IMF board, Mr Camdessus said: "The world economic outlook allows us to anticipate favourable trends for the world economy. I see it as my duty now to suggest you take advantage of these favourable circumstances to select my replacement."
The head of the IMF is traditionally a European and Britain would like the job.Mervyn King, Deputy Governor of the Bank of England, and Sir Nigel Wicks, a senior Treasury civil servant, are possible candidates, as is Andrew Crockett, head of the Bank for International Settlements.
The Chancellor, Gordon Brown - chairman of the IMF's interim committee - has been rumoured to be interested, although the Treasury has ruled this out.
Mr Brown paid tribute to Mr Camdessus yesterday before his resignation was announced, saying he "has led the IMF for almost 13 years, during which period there have been great changes in the world economy".
Other possible candidates for the job include Jean-Claude Trichet, France's central bank chief, and Philippe Lagayette, a French banker.
Mr Camdessus, 66, a former governor of the Bank of France, was not due to leave the job until 2002. But there had been considerable criticism of his performance in Washington, where the idea of a French Socialist in charge of the global economy did not please hardline Republicans.Reuse content