Signs that EU leaders might be coming together on a way to protect banks and contain the Greek debt crisis also helped drive the rebound, as traders looked past lackluster economic data in Europe and the United States.
In New York the WTI crude contract for November surged $4.01 to $79.68 a barrel.
In London, Brent North Sea crude headed back over the $100 a barrel line after dropping below it on Tuesday for the first time since early February.
The main London contract for November delivery ended at $102.73 a barrel, $2.94 higher from Tuesday.
Crude oil stocks fell by 4.7 million barrels last week, according to data from the Energy Information Administration, compared to expectations of a figure of around 700,000 barrels.
Nic Brown at Natixis credited a fall in oil imports, as well as the possibility that oil shipments are bypassing the Cushing, Oklahoma depot where many of the stocks are held.
Brown pointed out as well that total oil product demand was up by an unexpected 3.5 per cent year-on-year.
In Bucharest the government announced that two Irish firms have obtained oil and gas drilling rights in Romania.
Blackstairs Energy will drill in six blocs and Moesia Oil and Gas in one, Prime Minister Emil Boc said.
Seven blocs have been explored by Romania's Petrom, part of Austria's OMV group, and Romgaz, but they gave up on them after finding little oil and gas.
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