The Fed said it will spend $85 billion a month to sustain an aggressive drive to keep long-term interest rates low. It also plans to keep a key short-term rate near zero until unemployment drops below 6.5 percent.
Stimulus measures generally weaken the dollar, which tends to direct more investors into buying commodities.
Benchmark crude gained 98 cents to close at $86.77 a barrel in New York. It rose as high as $87.68 after the Fed's announcement.
Before the Fed statement was released Wednesday afternoon, oil was only moderately higher, with gains dampened by a big increase in the nation's gasoline supply. The government said gasoline supplies jumped by 5 million barrels last week, twice as much as analysts. That's a sign of weak demand.
Meanwhile, prices at the pump fell to $3.31 a gallon, about 4 cents higher than this day a year ago.
Brent crude, used to price international varieties of oil, rose $1.33 to $108.02 on the ICE Futures exchange in London.
Other futures on the New York Mercantile Exchange:
Heating oil rose 4 cents to $2.967 a gallon
Natural gas fell 3 cents to $3.382 per 1,000 cubic feet.
Wholesale gasoline rose 3.6 cents to $2.647 a gallon.