Following are their decisions put together in a "term sheet" on the ESM, which is to replace the existing fund the European Financial Stability Facility (EFSF) in mid-2013.
The term sheet now has to be prepared as a legal text of an amendment to the European Union treaty. Leaders want to sign the amended treaty by the end of June.
Before then, finance ministers will need to sort out some remaining technical details of the agreement and the overall deal will need parliamentary approval in several countries, including Germany and Finland.
LEGAL BASE
The ESM will be established by a treaty among euro zone countries as an intergovernmental organisation under public international law, based in Luxembourg.
PURPOSE
The ESM, with an effective lending capacity of 500 billion euros $709 billion, will rise funding and provide loans under strict conditions to euro zone states threatened by severe financing problems, to safeguard the stability of the euro zone.
GOVERNANCE
Euro zone finance ministers will be the board of governors of the ESM.
The board will also include the Economic and Monetary Affairs Commissioner and the president of the European Central Bank (ECB) as observers.
The ministers will decide on granting financial assistance, its terms and conditions, the lending capacity of the ESM and its instruments.
Decisions will be taken by qualified majority, with voting weights according to the subscriptions to ESM capital.
Qualified majority is defined as 80 percent of the votes.
CAPITAL STRUCTURE
The ESM will have a total subscribed capital of 700 billion euros, in order to secure a triple-A credit rating.
Of this amount, 80 billion euros will be paid-in capital. EU leaders agreed that the capital will be paid from 2013 over five years in five equal instalments.
This was a change, in response to German demands, to the initial deal by finance ministers, who had agreed that half of the capital would be paid in by July 2013 and the other half over the next three years.
The ESM will also have a combination of committed callable capital and guarantees from euro zone countries totalling 620 billion euros. The division between the callable capital and guarantees still needs to be sorted out.
The callable capital can be called in by euro zone finance ministers by a simple majority, when the paid-in capital has been reduced by the absorption of losses on loans made.
CONTRIBUTION KEY
Euro zone countries will contribute capital to the ESM on the basis of the ECB paid-in capital key.
But countries with a GDP per capita of less than 75 percent of the EU average will pay less for 12 years after joining the euro zone.
ESM AS PREFERRED CREDITOR
The ESM will have preferred creditor status, but will be junior to the IMF.
This shall be effective from July 1, 2013.
EFSF-ESM TRANSITION
Undisbursed and unfunded portions of existing loan programmes of the EFSF will be transferred to the ESM. EFSF and ESM consolidated lending shall not exceed 500 billion euros.
NON-EURO ZONE PARTICIPATION
Non-euro zone countries from the European Union can participate as lenders in ESM bailout programmes on an ad hoc basis.
The ESM does not provide loans for non-euro zone countries, which have their own balance of payments facility for emergencies, run by the European Commission.