A senior European Union official says a way has been found to get Greece more than €7 billion in short-term cash.
Valdis Dombrovskis, the EU Commission's vice president for the euro, said the 28-country bloc has approved €7.16 billion of bridge financing for Greece and that the money will come from funds in the European Financial Stabilisation Mechanism.
In a tweet, Mr Dombrovskis said the money should reach Greece by Monday.
Greece has a €4.2 billion payment due to the European Central Bank on Monday. Without the bridge financing it would not have been able to make the payment.
The agreement was announced shortly after the German parliament overwhelmingly backed another financial rescue.
As a result, expectations have risen that Greece will secure a three-year financial bailout which will allow it to get back towards some sort of economic normality following weeks of crisis which have seen banks shuttered and withdrawals at ATMs limited to €60 a day.
German policy-makers, following more than three hours of debate, voted 439-119 in favour of opening detailed discussions on the bailout package, after chancellor Angela Merkel warned that the cash-strapped country would face chaos without a deal.
"What we're witnessing is European solidarity in action," said Mr Dombrovskis. "Politicians across 27 countries have invested their own political capital to speed through national decisions to shoulder Greece at this difficult time for the country."
Though the broad outlines of the Greek bailout were agreed on Monday, specific terms will now be thrashed out between Greece and its European creditors.
The process is expected to last around four weeks and to lead to Greece getting around €85 billion to help it pay off upcoming debts.
Germany has been the largest single contributor to Greece's bailouts and has taken a hard line, insisting on stringent spending cuts, tax hikes and wide-ranging economic reforms in return.
"The principle ... of responsibility and solidarity that has guided us since the beginning of the European debt crisis marks the entire result from Monday," Ms Merkel told the special session of parliament.
The alternative to an agreement, she added, "would not be a time-out from the euro that would be orderly ... but predictable chaos".
Ms Merkel will have to return to parliament to seek approval for the final deal when the negotiations are concluded.
"I know that many have doubts and concerns about whether this road will be successful, about whether Greece will have the strength to take it in the long term, and no one can brush aside these concerns," she said. "But I am firmly convinced of one thing: we would be grossly negligent, even irresponsible, if we did not at least try this road."
Ms Merkel's finance minister, Wolfgang Schaeuble, who has talked particularly tough on Greece, said Germany will do its utmost to "making this last chance a success" - provided Greece does its part.
Bailing out Greece hasn't been popular in Ms Merkel's conservative bloc and 60 of its policy-makers failed to back her today, with another five abstaining.
In Athens, Greek prime minister Alexis Tsipras is widely expected to reshuffle his cabinet following a rebellion within his party over a parliamentary vote to approve the measures demanded for the bailout talks to start.
A little more than a quarter of the 149 MPs from Mr Tsipras's radical-left Syriza party either voted against or abstained in Wednesday's vote. He still won an overwhelming majority as three opposition pro-European parties backed the proposals.
The legislation, which includes consumer tax increases and pension cuts, was demanded as a pre-condition to the launch of negotiations on a third bailout. Elements of the bill are being implemented immediately, with changes to consumer tax coming into effect on Monday, the finance ministry said.
Also this week, the ECB raised emergency liquidity assistance to Greek banks.