Athens has pushed through controversial reforms which include restructuring family benefits, introducing a new process for foreclosures on overdue loans and making it more difficult to call a strike.
But the Greek government will still have to adopt the final round of “prior actions” demanded by international lenders before any new loans are issued.
The lenders claim Greece has only implemented 92 of the 110 agreed steps needed to receive loan payouts.
The new Eurogroup president, Portugal’s Mário Centeno, said the latest tranche from Greece’s third financial rescue programme since 2010 amounts to £5.89bn and will be used to cover debt servicing and arrears and to boost Greece’s cash reserves.
Mr Centeno said the cash injection was the most critical component of the package because it was “critical to ensuring Greece’s full market access”.
He said the eurozone would now start to look at cutting Greece’s debt which is equivalent to 180 percent of its annual economic output.
Mr Centeno said: “Looking ahead we can start with technical work on debt relief measures.
“The holistic growth prospect for Greece that we call upon is considered critical to making sure that the post programme status gains ownership in the country.”
Unemployment in the debt-ridden country is at more than 20 percent and pensioners have seen their income slashed by more than 30 percent.
The Greek economy was plunged into chaos after the 2007-2008 financial crisis and Athens sought international aid in 2010 to prevent the country from going bankrupt.
Greece has since received another two multi-billion-pound bailouts to keep public services running.
Prime Minister Alexis Tsipras was elected in 2015 after promising to end crippling austerity measures, which were a condition of the bailouts.
But he later signed up to a new £76billion package which expires in August.
He said his government had agreed to the latest austerity measures to ensure it receives the next tranche of bailout cash.