"In her first test before the U.S. Senate, she's come across clear and concise and saying what we expected," said Jones Trading Institutional Services analyst Yousef Abbasi.
Yellen reassured investors with comments on the Fed's $85 billion per month asset purchasing program, which is putting pressure on interest rates and providing liquidity in financial markets.
Speaking before the Senate Banking Committee, Yellen, who has been nominated to replace Fed Chairman Ben Bernanke in January, said it would be risky to withdraw from the quantitative easing program too soon, The Wall Street Journal reported.
"With the Yellen testimony out of the way, the market is going to be more comfortable putting capital to work," said Agam Kothari, director of equity trading at Citigroup.
On Wall Street, the Dow Jones industrial average closed at its 37th record high of the year, adding 54.59 points, 0.35 percent to 15,876.22.
The Standard & Poor's 500 index also hit an all-time closing peak, adding 8.62 points or 0.48 percent to 1,790.62.
The Nasdaq closed at 3,972.74, gaining 7.16 points, or 0.18 percent.
On the New York Stock Exchange, 2,001 stocks advanced and 1,056 declined on volume of 3.1 billion shares.
In Japan, the Nikkei 225 index added 309.25 points, or 0.8 percent, to 14,876.41.
In London, the FTSE 100 added 36.13 points, or 0.54 percent, to close at 6,666.13.
On currency markets, the euro traded lower at $1.3465 and the dollar rose to 99.96 yen.
The price for a barrel of crude oil gained 8 cents to reach $93.96 on the New York Mercantile Exchange.
On the Comex division of the New York Mercantile Exchange, the price of gold added $18.70 to hit $1,287.10 an ounce. Silver added 32.8 cents to hit $20.77.
Ten-year benchmark treasuries yielded 2.696 percent at the close of trading.
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