By early afternoon in Europe, benchmark oil for October delivery was up $1.84 at $100.15 a barrel in electronic trading on the New York Mercantile Exchange. The contract closed at $98.31, up $1.30, on Thursday.
In London, November Brent crude was up $1.75 at $117.63 a barrel on the ICE Futures exchange.
The Fed said it will spend $40 billion a month to buy mortgage-backed securities for an indefinite period. The purchases are intended to lower long-term interest rates to spur borrowing and spending.
The Fed also extended a plan to keep short-term interest rates at record-low levels through to mid-2015, as it attempts to boost an economy it says is too weak to reduce high unemployment.
Expectations of action by the Fed, as well as the European Central Bank and China's government, have balanced gloomy economic news and kept oil in a narrow range the past few weeks.
Oil analyst Stephen Schork said that the Fed decision was tantamount to "flooding the market with dollars," which weakens the American currency and helps make crude a cheaper and more attractive investment for traders using other currencies.
On Friday, the euro was up to $1.3107 from $1.2987 late Thursday in New York.
"With additional liquidity looking for a home, commodity markets are bound to benefit given prevailing ultra-low global interest rates," said Economist Intelligence Unit commodities analyst Caroline Bain. "From a more fundamental perspective, further monetary easing in the U.S. should be positive for U.S. economic growth and wider global growth in as much as higher U.S. aggregate demand provides stimulus across the world."
Traders on Friday also kept a close eye on unfolding unrest in the oil-rich Middle East.
Protesters stormed the U.S. Embassy compound in Yemen's capital Thursday. Ongoing clashes have been taking place around the U.S. mission in Cairo, and the U.S. ambassador to Libya was killed Tuesday.
"The oil market now simply needs some little geopolitical spark to attract the financial flows," said analyst Olivier Jakob of Petromatrix in Switzerland.
In other Nymex trading, gasoline was up 5.3 cents at $3.0152 a gallon and heating oil added 4.71 cents to $3.2584 a gallon. Natural gas advanced 1.7 cents to $3.054 per 1,000 cubic feet.
Pamela Sampson in Bangkok contributed to this report.