The fund, which will be called the European Stability Mechanism (ESM) will replace the current 440bn euro European Financial Stability Facility (EFSF).
The EFSF was set up last year to provide support to eurozone countries.
The agreement comes a month ahead of expectations, and is one of many decisions to be made on the fund.
The new ESM will be part of a "comprehensive package" of measures European leaders are hoping to agree in late March to resolve the eurozone debt crisis that has overshadowed the region for the past year.
The chairman of eurozone finance ministers, Jean-Claude Juncker, told a news conference: "We've already agreed on the volume of the lending capacity of the ESM. We've agreed on the amount of 500bn euros, and this will be subject to regular revision."
The current EFSF, which was designed as a temporary facility to last until 2013, has a notional 440bn euros at its disposal but in reality can only lend out about 250bn euros because of the amount it has to keep back in order to be strong enough to keep its borrowing costs low.
Mr Juncker said that the 500bn euros promised to the new mechanism would constitute its effective lending capacity.
Apart from the eurozone, the new ESM would also get cash from the International Monetary Fund (IMF) and, possibly, from voluntary contributions from non-euro one European Union countries. These matters have not yet been discussed.
The Economic and Monetary Affairs Commissioner, Olli Rehn, said: "The unwritten understanding with the IMF is that there can be 50 cents to one euro that the Europeans have themselves contributed to such operations as we have for instance in the cases of Greece and Ireland."
That would imply a potential IMF contribution of 250bn euros, the same amount as is currently available.
Current support also includes 60bn euros from the European Financial Stability Mechanism (EFSM).
Mr Juncker warned that decisions about the ESM were in their early stages: "What I'd like to say is that both the EFSF and ESM are not the subject of overall agreement until everything is agreed. Nothing is agreed until everything is agreed."