The two sides have agreed a batch of reforms that will be presented to the Greek Parliament on Thursday.
The eurozone countries insisted on the measures before releasing €2bn (£1.4bn) in loans and up to €10bn in support for the banks.
The agreement will help pave the way for further payments under the country's third bailout.
The eurozone has agreed to provide Greece with up to €86bn in total.
Like the first two bailouts, the third, which was agreed in July, came with an extensive list of conditions that Greece had to meet before it receives instalments of the loans.
It has so far received €13bn under the third programme.
The next payment had been held up by differences between the two sides over protection from repossession for home owners in arrears with their mortgages and about reforms to the banks.
These and other issues have now apparently been resolved although Greece still has work to do to put the measures it has agreed into effect.
Of the €12bn of delayed funds, €2bn is for general support for the Greek government budget. The remainder is for recapitalising the banks - repairing their financial foundations so that they can function effectively.
The banks are also asking private investors to come up with some cash, but a contribution from the bailout will also be needed.
The Greek Finance Minster Euclid Tsakalotos described it as a difficult negotiation and said the pressure to get the deal finalised came from the need to support the banks.
The eurozone has also held out to Greece the possibility of debt relief after a review of progress under the new bailout.
However, it has said that relief would come in the form of longer delays before repayments start or finish, not a reduction - or so-called "haircut" - in the amount that has ultimately to be repaid.
Greece has secured a tentative deal with the eurozone to unlock the latest tranche of financial aid.