For months, the bailout discussions have stalled amid disagreements over what reforms, including to pensions, tax and the labour market that Greece should take in order to get the rescue money due from its most recent international rescue.
Without the money, Greece would once again be facing the prospect of having to exit the eurozone so-called Grexit.
"The big blocks have now been sorted out and that should allow us to speed up and go for the final stretch," Jeroen Dijsselbloem told reporters following a meeting of the eurozone's 19 finance ministers in the Maltese capital of Valletta.
EU Commission Vice-President Valdis Dombrovskis said a deal on the latest steps to keep Greece afloat should be within reach by the time the eurozone ministers meet again on May 22 easily in time for Greece's next big debt-repayment hump in July.
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Another key development today appears to be the ongoing involvement of the International Monetary Fund, which has been part of Greece's bailout programs since the first rescue back in 2010.
"There is agreement on these main topics, on these big reforms, on the size sequencing and the timing that is with the IMF absolutely yes," Dijsselbloem said. "I could not talk about an agreement on those issues if the IMF had not agreed."
The broad outlines of today's agreement involve Athens making further economic reform commitments until 2020.
Without the loan, Greece would struggle to make a debt payment in July, raising anew the prospect of default. The last time, Greece faced potential bankruptcy was in July 2015, when the Tsipras government eventually agreed a three-year bailout that could amount to 86 billion euros (USD 91 billion).
Today's developments appear to have put paid to that threat.
Tsipras had blamed unnamed negotiators among Greece's European creditors and the International Monetary Fund for "moving the goalposts" each time Greece was close to meeting approval conditions for the bailout.
Even Wolfgang Schaeuble, the German finance minister who has been one of Greece's sharpest critics over the past few years, said he didn't expect any major hitches ahead. "The longest distance is behind us," he said.
But the talks have dragged on for months, freezing the latest loan payout and hurting the chances of a self-sustaining Greek economic recovery after years of recession and turmoil.
Tsipras' left-led government is pushing for a comprehensive deal that would cover more than just spending cuts and reforms by Greece, but also alleviate the country's debt burden and pave the way for its return to international bond markets later this year.
Greece has depended on international bailouts since 2010 after it was unable to borrow on international bond markets.
Dijsselbloem conceded that the failure to agree the release of the next batch of bailout funds had harmed Greece's economic recovery in recent months.
"That momentum is slipping away from us so we really need to work fast and have it done certainly well in time for the next payments Greece has to make," Dijsselbloem said.
Currently demanded cutbacks include new pension cuts, a broadening of the tax base, labor reforms and privatizations. These will require approval by Greece's parliament, where Tsipras holds a three-seat majority.
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