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The tech-rich Nasdaq added 22.34 points (0.78%) at 2 869.88, the highest close since December 2000, when it was plummeting as the dot-com bubble famously burst, plunging the country into recession.
Riding news that the Fed would not raise ultra-low interest rates, the Dow Jones Industrial Average also surged, adding 95.59 points (0.76% ) to finish at 12 690.96.
The broad-market S&P 500 advanced 8.42 points (0.62%) to 1 355.66.
The blue-chip Dow and the S&P 500 finished at their highest levels since 2008, in May and June, respectively.
The Fed left the door open for more economic stimulus while saying its current $600bn program to inject liquidity into the economy would be allowed to run its forecast course through June.
The dollar fell sharply against the euro, however, as Bernanke reiterated the economy's weaknesses and need for low rates despite rising inflation, in a first-ever press conference following a meeting of the central bank's policy-making panel.
By the end of Bernanke's one-hour meeting with journalists, the euro was at $1.475, compared with the average level of about $1.467 during the morning and $1.464 late Tuesday.
Bernanke told reporters that the country face a huge problem in its massive debt load.
"It's the most important economic problem, at least in the longer term, that the United States faces," he said.
"US stocks moved solidly higher on the day, after receiving a nice afternoon jolt from the comments of Fed chairman Ben Bernanke in the inaugural post-policy meeting news conference," Charles Schwab analysts said in a client note.
Helping to underpin the market, on the ninth day of a solid rally, was a report that durable goods orders had risen 2.5 percent in March, a sign that US industry continues to expand and companies are investing in and upgrading equipment.
The bond market slumped. The yield on the 10-year Treasury rose to 3.37% from 3.32% late on Tuesday.
Bond yields and prices move in opposite directions.
