Apple's 2% rise propped up all three major indexes and helped the S&P 500 extend gains for the year.
Yellen, who made her first remarks since the Fed held steady on rates earlier this month, said inflation in the United States had not yet reached sustainable levels amid uncertainty about China's economy and low oil prices.
Yellen's stance contrasts with recent comments from other policymakers who have voiced support for more than one increase this year.
Global markets cheered Yellen's remarks, which suggested that a rate hike was not immediately on the horizon. The dollar fell more than a%, while bond prices rallied.
"Yellen's comments allowed investors to breathe a sigh of relief that the Fed will not be raising rates in April," said Sam Stovall, U.S. equity strategist at S&P Global Market Intelligence in New York.
Stovall said the Fed would focus on data to see whether a hike in June would be possible.
Traders see a 26% chance that the Fed will make a move on rates at its meeting in June, according to the CME Group's FedWatch program.
Crude oil rose more than 2% as the dollar weakened and a report showed a less-than-expected build in U.S. crude stockpiles last week.
Data on Wednesday showed the U.S. private sector added more jobs than expected in March. The report, by payrolls processor ADP, serves as a precursor to the more comprehensive non-farm payrolls data on Friday.
At 9:36 a.m. ET (1336 GMT), the Dow Jones industrial average was up 110.61 points, or 0.63%, at 17,743.72, the S&P 500 was up 10.68 points, or 0.52%, at 2,065.69 and the Nasdaq Composite was up 31.88 points, or 0.66%, at 4,878.51.
Nine of the 10 major S&P sectors were higher, led by a 0.83% rise in the energy sector. Chevron was up 1%.
Apple was up 2% at $109.80 after Cowen raised its rating on the stock to "outperform".
Lululemon shares were up 8.3% at $66.36 after the Canadian yogawear retailer reported higher-than-expected quarterly net profit.
Valeant was up 3.3% at $29.92 after the Canadian drugmaker sought a waiver to a condition in its credit facility and said it was comfortable with its liquidity position.
Carnival Corp was up 4.1% at $51.70 after the cruise operator reported results.
Advancing issues outnumbered decliners on the NYSE by 2,170 to 489. On the Nasdaq, 1,737 issues rose and 473 fell.
The S&P 500 index showed 40 new 52-week highs and no new lows, while the Nasdaq recorded 49 new highs and five new lows.
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