The European single currency reached $1.4882 -- the highest point since December 7, 2009. It later stood at $1.4834 compared with $1.4785 late in New York on Wednesday.
Against the Japanese currency, the dollar dropped to 81.63 yen from 82.15 late Wednesday.
The dollar's tumble sent 'safe-haven' gold to an all-time of $1,534.05 an ounce.
"The highlight in the day ahead will be the first reading on Q1 US GDP," said RBC Capital Markets analyst Sue Trinh.
The first-quarter US gross domestic product (GDP) data comes a day after the Fed said it would hold interest rates at 0-0.25 percent "for an extended period".
"The Fed is clearly not thinking about tightening policy anytime soon and, from this perspective, there was nothing in the Fed's language to arrest the US dollar's recent decline," noted Spiros Papadopoulos of National Australia Bank.
The policy-setting Federal Open Market Committee (FOMC) also signalled it would maintain its $600 billion stimulus programme through June as originally planned.
Fed chairman Ben Bernanke indicated that after this round of spending the bank would leave the current level of stimulus in place, as it assesses whether the economy is strong enough to thrive on its own.
Gen Kawabe, dealer at Chuo Mitsui Trust and Banking, said: "While the Fed's decision was in line with the market's expectation, Bernanke's remarks gave rise to a view that the Fed will continue its monetary easing for a prolonged period, spurring dollar selling and stock purchases."
Since the 2008 financial crisis the Federal Reserve has lapped up assets, nearly tripling its holdings and pumping almost $1.8 trillion extra into the economy in the process.
Bernanke said that level "should essentially remain constant going forward from June," while hinting that further spending was off the table for now.
"The trade-offs -- are getting less attractive at this point," he said.
In London on Thursday, the euro changed hands at $1.4834 against $1.4785 late in New York on Wednesday, at 121.10 yen (121.49), £0.8904 (0.8890) and 1.2951 Swiss francs (1.2932).
The dollar stood at 81.63 yen (82.15) and 0.8730 Swiss francs (0.8744).
The pound was at $1.6658 (1.6626).
On the London Bullion Market, gold prices stood at $1,531.07 an ounce compared with $1,511 late Wednesday.-AFP