Eurozone ministers have agreed to give Greece a €7bn (£5bn) bridging loan from an EU-wide fund to keep its finances afloat until a bailout is approved.
The loan is expected to be confirmed on Friday by all EU member states.
In another development, the European Central Bank (ECB) agreed to increase emergency funding to Greece for the first time since it was frozen in June.
The decisions were made after Greek MPs passed tough reforms as part of a eurozone bailout deal.
The bridging loan means Greece will be able to repay debts to the ECB and IMF on Monday.
Greek banks, which have been closed for nearly three weeks, could also reopen on Monday, Greek media reported, although credit controls will remain in place.
Eurozone leaders agreed on the bailout in principle in Brussels on Monday, on the condition that the Greek parliament passed reforms on taxation increases and pension curbs by Wednesday.
The €7bn bridge loan was agreed in a conference call on Thursday to tap the EU's EFSM emergency fund.
Britain, which is in the EU but not the eurozone, later said it had won an agreement to protect UK money in the EFSM.
Chancellor of the Exchequer George Osborne said the concession would also apply to other non-eurozone states.
At a news conference on Thursday, ECB President Mario Draghi said emergency funding - ELA - to Greek banks was being raised by €900m over one week.
"Things have changed now," he said. "We had a series of news with the approval of the bridge financing package, with the votes, various votes in various parliaments, which have now restored the conditions for a raise in ELA."
Analysis by Chris Morris, BBC Europe correspondent
The European institutions are now picking up the pace to make sure this rather chaotic show stays on the road.
There's more emergency funding for Greek banks from the ECB. And agreement on a €7bn bridging loan from the EFSM to get the Greek state through the next few days.
Greece needs to repay €4.2bn euros to the ECB on Monday, as well as making up all its missed payments to the IMF. In other words it needs to spend the €7bn almost as soon as it gets it.
Some creative financial engineering has ensured that short-term funding from the EFSM will get final approval tomorrow. And then attention will turn to negotiations on the three-year bailout programme that Greece has applied for.
Those negotiations are likely to last for weeks, and plenty of things can still go wrong.
There's scepticism in Greece that the deal is too tough; scepticism elsewhere that it isn't tough enough.
Even today, the German Finance Minister Wolfgang Schaeuble has repeated his suggestion that maybe a "time-out" from the eurozone would be the best thing for Greece.
It is pretty unprecedented language. And it suggests that the battle to keep Greece in the eurozone is far from over.
Greek Prime Minister Alexis Tsipras won the parliamentary vote in the early hours of Thursday by 229 votes to 64, but needed the support of opposition MPs to do so.
His left-wing Syriza-led government is expected to survive, despite losing its majority after 38 Syriza MPs rejected the reforms.
It paves the way for eurozone finance ministers to open detailed talks on the bailout, worth up to €86bn, and on Thursday they said they agreed "in principle" to start negotiations.
Finland's parliament on Thursday approved the bailout talks - one of a number of eurozone states which require a mandate from their own parliament for Greece to secure new funds.
Germany's parliament is due to vote on the deal on Friday.
Passionate opposition came from within Mr Tsipras's own Syriza party, with parliamentary speaker Zoe Constantopoulou calling the measures "social genocide".
Former Finance Minister Yanis Varoufakis was another vocal opponent.
In his address to parliament Mr Tsipras said: "I acknowledge the fiscal measures are harsh, that they won't benefit the Greek economy, but I'm forced to accept them."
Since capital controls were imposed and the banks shut on 29 June, Greeks have been limited to withdrawing €60 a day.
German Finance Minister Wolfgang Schaeuble, known for his hardline approach, told national radio he would submit a request for parliament to reopen negotiations on the third bailout with "full conviction".
What happens next?
- EU member states to back eurozone decision on €7bn bridge loan to clear Greece's immediate debts (expected Friday)
- German parliament to back negotiations on €86bn eurozone bailout deal (Friday)
- Greek parliament to pass further reforms (22 July)
- Lengthy eurozone talks to start on bailout through European Stability Mechanism
But he also said he believed a temporary "Grexit" - Greece leaving the eurozone - would perhaps be a better option.
By 22 July, Greece must also commit to a major overhaul of the civil justice system. It has to agree to more privatisation, to review collective bargaining and industrial action, and make market reforms, including Sunday trading.
The vote in the early hours of Thursday approved:
- VAT changes including a top rate of 23% to take in processed food and restaurants; a 13% rate to cover fresh food, energy bills, water and hotel stays; and a 6% rate for medicines and books
- An increase in corporation tax from 26% to 29% for small companies
- An increase in luxury taxes on big cars, boats and swimming pools
- An end to early retirement by 2022, increasing the retirement age to 67
Opponents of the bailout measures took to the streets of Athens in mainly peaceful protests ahead of the vote on Wednesday. However, one group threw petrol bombs at police officers who responded with tear gas.