The cheer however was tempered by expectations the bailout will not be a cure-all for Greece's problems and the reforms Athens must implement in exchange will be painful.
Analysts also said the initial panic sparked by Iran's decision to halt its oil sales to France and Britain was dissipating after traders realised it was part of Tehran's brinkmanship strategy.
New York's main contract, light sweet crude for delivery in March was $1.70 higher at $104.94, and Brent North Sea crude for April delivery gained 21 cents to $120.26 in morning trade.
"Obviously there's a cheer in Europe over the news in Greece... but Iran is raining on their parade," said Justin Harper, head of research at IG Markets Singapore.
"And there's still a long way to go for Europe and Greece, so it's not really time to celebrate yet," he told AFP.
"I think with the Brent (contract), the initial panic over Iran is going away... people are actually calming down after realising that this is a game of political brinksmanship from Iran."
Despite the deal with Athens, "there are still uncertainties in Europe and Greece," Harper noted.
"Greece may need a third bailout so it's a long time before we see demand in Europe come up again."
The deal came after 12 hours of tense talks in Brussels that saw Greek Prime Minister Lucas Papademos -- a former European Central Bank No. 2 -- act as go-between for ministers with negotiators for private creditors.
The deal will bring government debt in Athens down to "120.5 percent" of gross domestic product (GDP) by 2020, a eurozone governmental source told AFP.
The figure is just a fraction above the 120-percent target set by the European Union and International Monetary Fund, and means a 5.5-billion-euro gap in funding was reached to bring it down from an estimated 129 percent.
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