Wheat futures at the Chicago Board of Trade, which have increased more than 10 percent in about a week, were also supported by concerns that Russia's wheat crop could be hurt by lower-than-normal temperatures in some growing areas in the country, the world's third largest exporter of the grain in the current season.
There was also support from expectations for Russia to curb exports to ensure sufficient supplies at home.
Grains have also been finding support in surging prices in the cash markets fueled by farmers holding out for higher prices and a pick up in export demand after a recent slump in prices. Corn was bid at $1.00 per bushel premium to CBOT March corn futures in the export market on Thursday as a shipper scrambled to secure supplies to fill a waiting vessel.
The Fed's decision to keep interest rates near zero into 2014 and suggestion the bank was ready to provide more stimulus if the economy deteriorates supported risk assets like grains as investors bailed out of the dollar.
"This is all driven by outside markets. The (grain) fundamentals are the same as they were yesterday," said Karl Setzer, analyst at the MaxYield Cooperative in West Bend, Iowa.
Chicago Board of Trade wheat futures surged more than 2 percent to a three-week high while corn futures gained about 1 percent to a two-week top.
"The wheat market was heavily short and they're covering and no one really knows if or how much damage cold weather did in Russia," said Paul Haugens, vice president for Newedge USA.
A weaker US dollar makes commodities priced in the greenback more attractive to importers. Export demand for each crop has been growing in recent weeks, with US Agriculture Department export sales results data on Thursday showing wheat exports the largest in four months and corn the biggest in three months.
Noncommercial investors, such as hedge funds, held a record-large short position in CBOT wheat futures as of last week, which has helped precipitate rallies in recent days as investors buy back futures they sold to guard against further gains in prices.
CBOT March wheat was up 2.3 percent, or 14-1/2 cents, at $6.55-3/4, while CBOT March corn was 5-1/2 cents higher at $6.40 per bushel and CBOT March soybeans 11-1/4 cents higher at $12.24-3/4.
"Export demand is strong, which is also supportive," said Citigroup analyst Terry Reilly. "There's a lack of sellers and fund short-covering in wheat."
Wheat futures have increased 11 percent from their lows last week. Corn futures gained 8 percent from their low and soybeans about 6.5 percent.
Prices in the cash grain markets were strong. Basis bids -- the amount over or under benchmark futures that grain merchants are willing to pay for supplies -- were near record highs for this time of year in the US Midwest.
Basis bids for corn barges near export elevators at the US Gulf Coast surged on Thursday as at least one short-bought grain shipper scrambled for immediate supplies to load a cargo ship waiting in port, trade sources said.
However, the strong basis and higher futures were likely to spur some farmer sales on Thursday and that could put a lid of futures despite the friendly outside markets.
"When you have producer sales, you'll see futures under a little pressure, so we'll probably see some choppy trade today," Reilly said.
World stocks, oil and gold all gained on Thursday after the Fed set out an unambiguously easier policy stance, but fears of a messy Greek debt default kept investors' enthusiasm in check.
Analyst ProAgro said on Thursday major exporter Ukraine's grain harvest was likely to come in at about 40 million tonnes in 2012, down from a record of 56.7 million tonnes in 2011 due to a fall in acreage due to bad weather while winter crops were being sown.