New York's main contract, light sweet crude for delivery in December, added 30 cents to 79.35 dollars a barrel.
Brent North Sea crude for December delivery gained 41 cents to 77.91 dollars per barrel in London trading.
The US government's Department of Energy will later publish a report on American crude oil stockpiles for the week ending November 6.
"Oil continues to flirt with the 80-dollar level and not quite having the conviction to push on higher, but this afternoon's inventory numbers could be just what the bulls are after to test resistance levels," said Capital Spreads analyst Simon Denham.
Crude oil futures had fallen on Tuesday as Hurricane Ida fizzled into a tropical depression, easing worries about the potential threat to petroleum installations in the Gulf of Mexico.
Oil and gas operations have now restarted in the area after closing down ahead of the onset of Hurricane Ida, the Commonwealth Bank of Australia said in a report.
"Offshore oil and gas operators in the Gulf of Mexico are reboarding platforms and rigs and restoring production" as any potential threat from Hurricane Ida had passed, the US Minerals Management Service (MMS) said.
The MMS said 43 percent of US oil production in the Gulf had been shut down due to the storm.