"Approval is now given, national procedures will be finalised by Monday noon," one senior eurozone official said, referring to the transfer of €4 billion from the currency zone.
Greece adopted on Thursday the last piece of legislation international lenders required to unlock a total of €5.8 billion in aid from the euro area, its national central banks and the International Monetary Fund.
Deputies of eurozone finance ministers approved the payment at a conference call Friday morning.
Germany this week postponed signing off on the disbursement until next Monday to ensure all conditions are met, but officials said German approval was now a mere formality.
The latest tranche includes €2.5 billion from the eurozone's EFSF rescue fund, €1.5 billion of bond profit returns from eurozone central banks and another €1.8 billion from the IMF.
Subject to implementation of further reforms, Athens stands to receive another €1 billion in October.
Thursday's vote resolved the latest negotiation round between Athens and its lenders, which started in early June and stretched to the limit the cohesion of its shaky government.
Prime Minister Antonis Samaras's abrupt decision in June to shut down state broadcaster ERT to meet public sector dismissal targets caused the departure of a coalition ally, leaving him with a parliamentary majority of five seats.
The country's reform record has been patchy ever since its EU/IMF bailout started in mid-2010, leading to frequent delays in the disbursement of rescue funds.
The troika of international lenders will return in Athens in the autumn to find out whether the government needs to find further savings to meet its 2015-2016 budget targets.
Setting the stage for a potential clash with lenders, Samaras and his only remaining coalition partner, Socialist leader Evangelos Venizelos, have ruled out any further austerity measures.
Opposition to the bailout has intensified as the country goes through its sixth year of recession and unemployment hovers at a record rate of 27%.
Bailout money for Athens runs out at the end of 2014 and the country is expected to need further relief to make its debt sustainable - even though it has already received about 90% of the €240 billion earmarked to protect it from a chaotic default and possible exit from the eurozone.
