New York's main contract, West Texas Intermediate (WTI) or light sweet crude for April, gained $1.46 to close at $106.16 a barrel.
In London trade, Brent North Sea crude for April settled at $124.12 a barrel, surging $2.14 from Tuesday's closing level.
Crude futures had fallen sharply on Tuesday, shedding about $2 on the back of worries over Greece's massive bailout deal and dimmer economic growth prospects in China and Europe.
But an improved picture for the Greek deal and the report on the US central bank helped turn around sentiment.
"Crude was boosted by a story in the Wall Street Journal that the Fed was considering a fresh variation on its bond-buying program, once again raising speculation of further central bank stimulus," said GFT markets analyst David Morrison.
"Investors are so desperate for signs of further Fed intervention that they are jumping on anything," he added.
The energy market also remained underpinned by ongoing tensions between the West and major crude producer Iran over its nuclear program.
Iran has repeatedly denied that it is building an atomic bomb, saying the program is for peaceful purposes.
The closely watched weekly US energy stockpiles report Wednesday was mildly bullish for oil prices.
The US Department of Energy said crude inventories grew 800,000 barrels in the week to March 2, less than traders had anticipated.
What the stars mean:
★ Poor ★ ★ Promising ★★★ Good ★★★★ Very good ★★★★★ Exceptional