The loan is expected to be confirmed on July 17 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 lawmakers 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 July 20.
Greek banks, which have been closed for nearly three weeks, could also reopen on July 20, Greek media reported, although credit controls will remain in place.
Eurozone leaders agreed on the bailout in principle in Brussels on July 13, on the condition that the Greek parliament passed reforms on taxation increases and pension curbs by July 15.
The €7 billion bridge loan was agreed in a conference call on July 16 to tap the EU’s EFSM emergency fund.
At a news conference on July 16, ECB President Mario Draghi said emergency funding – ELA – to Greek banks was being raised by €900 million 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.”
Greek PM Alexis Tsipras won the parliamentary vote in the early hours of Thursday by 229 votes to 64, but needed the support of opposition lawmakers to do so.
His left-wing Syriza-led government is expected to survive, despite losing its majority after 38 Syriza lawmakers rejected the reforms.
It paves the way for eurozone finance ministers to open detailed talks on the bailout, worth up to €86 billion, and on July 16 they said they agreed “in principle” to start negotiations.
Finland’s parliament on July 16 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 July 17.
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