A softer greenback makes dollar-priced oil cheaper, leading to higher demand and pushing the cost of crude higher.
In morning Asian trade, New York's main futures contract, light sweet crude for June, rose 61 cents $113.37 a barrel, while Brent North Sea crude for delivery in June gained 62 cents to $125.75.
"Oil prices are heading up... as a result of the US Federal Reserve Bank providing reassurance on the US economy, so markets started to rally," said Victor Shum, a Singapore-based analyst at Purvin and Gertz energy consultancy.
The Federal Reserve said Wednesday it would maintain its key interest rate at zero to 0.25 percent to support economic growth.
Citing the economy's only "moderate" recovery, the central bank also kept the door open for more economic stimulus, while saying its current $600 billion programme would be allowed to run its forecast course through June.
Keeping low interest rates however will drive investors away from US assets as they seek higher yielding investments elsewhere, causing the dollar to weaken.
The market was also pressed by political developments in the oil-producing Arab world, analysts said.
Foreign pressure is mounting on Syrian President Bashar al-Assad, while hundreds of members resigned from his party and government troops kept their grip on the flashpoint town of Daraa.
In Yemen, President Ali Abdullah Saleh said he supported "peaceful" change in line with the country's constitution as at least 15 more people were killed and more than 130 wounded on Wednesday with no let-up in protests.
And in Libya, the country's tribes urged strongman Moamer Kadhafi to cede power, as rebels backed by NATO air strikes said they drove the veteran leader's forces out of missile range of the lifeline port of Misrata.