The Dow Jones Industrial Average closed 1.1% higher at 15,460.92 and the broader S&P 500 added 1.3% to end at a new peak of 1,675.02.
Both measures surpassed previous record highs hit in late May.
Investors have been focusing on when the Fed might end its massive bond-buying programme.
Fed chairman Ben Bernanke had made previous comments suggesting the policy would be phased out.
But on Wednesday Ben Bernanke clarified his position, saying a “highly accommodative” policy was needed for the foreseeable future.
Since late last year, each month the Fed has been buying $85 billion in Treasury and mortgage bonds.
The purchases have kept interest rates low, with the aim of encouraging more Americans to buy homes and cars, and hopefully bolster economic growth.
Investors worry that once the Fed starts scaling back its bond buying, interest rates will rise.
“The Fed has made it unequivocally clear that they are not in any hurry to do anything,” said Alec Young, Global Equity Strategist at S&P Capital IQ.
“It’s very bullish for stocks,” he added.
The S&P 500 index has risen for six trading sessions in a row, the longest winning run in four months.
The Nasdaq composite rose 1.4% on Thursday to close at 3,578.30, its highest level in almost 13 years.
Microsoft was one of the biggest winners on the stock market on Thursday.
Its shares jumped 2.8% after the company announced a plan to overhaul its structure.
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