The European single currency reached $1.4882 -- the highest point since December 7, 2009. It later stood at $1.4815 compared with $1.4785 late in New York on Wednesday.
Against the Japanese currency, the dollar dropped to 81.47 yen from 82.15 late Wednesday.
The dollar's tumble sent 'safe-haven' gold to an all-time of $1,538.48 an ounce.
With the Fed saying Wednesday it would hold interest rates at 0-0.25 percent ‘for an extended period’ the dollar came under renewed pressure.
‘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.
The announcement of a sharp deceleration in US growth to 1.8 percent in the first quarter as the government slashed spending had little effect on the greenback as the result was in line with economists' estimate.
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.’
‘The current dollar weakness is mainly due to the Fed's expansionary monetary policy,’ said Commerzbank.
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.
On the London Bullion Market, gold prices stood at $1,535.50 an ounce compared with $1,511 late Wednesday.
‘Gold prices gained 1.4 percent to close at a fresh all-time high at $1526.4 an ounce buoyed by the dollar weakening against the euro to levels not seen since December 2009, higher oil prices, inflationary fears amid stronger equity markets and a low interest rate environment,’ said Suki Cooper at Barclays Capital.
In London on Thursday at 1600 GMT, the euro changed hands at $1.1.4815 against $1.4785 late in New York on Wednesday, at 120.70 yen (121.49), £0.8895 (0.8890) and 1.2927 Swiss francs (1.2932).
The dollar stood at 81.47 yen (82.15) and 0.8725 Swiss francs (0.8744).
The pound was at $1.6654 (1.6626).