The eurozone emergency fund agreed on Friday (7 July) to unblock a €8.5 billion new tranche of loan for Greece, as part of the bailout programme agreed in 2015.
The fund, known as the European Stability Mechanism (ESM), is expected pay out a total of €7.7 billion on Monday.
Some €6.9 billion will help Greece to meet its debt repayment commitment, which amounts to around €7 billion this month, while €800 million will be used to clear arrears.
The second part, €800 million, will be paid in September if the Greek government has made "significant progress on arrears clearance" with its own funds, the ESM said in a statement.
The ESM took the decision after Greece implemented all the measures it had agreed with its creditors in recent months.
In May, Greece reached an agreement with the European Commission, the European Central Bank (ECB), the ESM and the International Monetary Fund (IMF) on measures - mainly pension and tax reforms - to save around €4 billion by 2020.
In June, eurozone finance ministers had agreed on the amount of the new tranche of aid after an agreement in principle with the IMF over debt relief measures for Greece – which will be specified later.
The ESM payment, due at the end of June, was postponed until Greek authorities had cleared several issues – for example, on whether shops should open on Sunday, or legal cases on pension reforms.
Eurogroup president Jeroen Dijsselbloem said on Twitter that the payment was the "next important step" for Greece, and stressed that is was the "result of joint efforts".
"This payment is recognition of the tremendous efforts that the Greek people have continued to make to stabilise their economy," EU finance commissioner Pierre Moscovici said in a statement.
The payment marks the end of several months of tensions to conclude the so-called second review of the bailout programme, which should have completed more than a year ago.
The Greek government had resisted cuts in pensions, while Germany opposed debt relief measures required by the IMF to continue its participation in the programme.
Last month, the IMF promised a $2-billion loan (€1.8 billion) to Greece, which will be disbursed when specific debt relief measures have been defined. The measures will be implemented at the end of the programme, in 2018, if Greece has completed all of the programme.
The board of the IMF is expected to endorse the plan before the end of the month.
An EU official noted this week that the next Eurogroup meeting, on Monday (10 July), will be the first for a long time without Greece on the agenda.