Sentiment also got a boost from higher oil prices following US inventory data showing a big drop in petroleum supplies.
Yellen, appearing in a twice-annual hearing on Capitol Hill, reaffirmed the US central bank's plan for gradual rate hikes, as long as the economic data remains solid.
But Yellen noted that inflation lags the Fed's 2 percent target.
The overall impression "eased some of the rate-hike concerns that surfaced last week following the release of the FOMC minutes from the June meeting, which initially left the impression that the Fed plans to press on with a tightening of policy despite the persistence of below-target inflation data," said Briefing.com.
The Dow rose 0.6 percent to finish at its first record since June 19.
European equities also closed strong, with Paris, London and Frankfurt all winning at least one percent.
But the dollar retreated against the pound and yen after Yellen adopted a more dovish line than some expected.
"At the end of the day, the Fed is still telling us rates will rise again but September is off the table," said Kathy Lien, managing director of BK Asset Management.
Oil prices pushed higher after US inventory data showed a 7.6 million barrel decline in petroleum inventories.
That lifted shares of BP rose 1.9 percent, Italian oil giant Eni added 1.7 percent and Dow-member Chevron was up 0.8 percent.
Technology shares were also were strong, with Facebook jumping 2.3 percent, Google-parent Alphabet 1.5 percent and Microsoft 1.7 percent.
Amazon gained 1.3 percent as it hailed a successful Amazon Prime shopping day on Wednesday, saying it attracted more new members to the subscription service than on any previous day.
Airline shares were lifted after American Airlines said second-quarter revenue per seat mile had risen 5 to 6 percent from the year-ago period, a better range than previously.
American Airlines rose 4.2 percent, Delta Air Lines gained 2.2 percent and United Continental 4.7 percent.
KEY FIGURES AROUND 2045 GMT (4:45 a.m. Thursday in Manila)
New York - DOW: UP 0.6 percent at 21,532.14 (close)
New York - S&P 500: UP 0.7 percent at 2,443.25 (close)
New York - Nasdaq: UP 1.1 percent at 6,261.17 (close)
London - FTSE 100: UP 1.2 percent at 7,416.93 (close)
Frankfurt - DAX 30: UP 1.5 percent at 12,626.58 (close)
Paris - CAC 40: UP 1.6 percent at 5,222.13 (close)
Tokyo - Nikkei 225: DOWN 0.5 percent at 20,098.38 (close)
Hong Kong - Hang Seng: UP 0.6 percent at 26,043.64 (close)
Shanghai - Composite: DOWN 0.2 percent at 3,197.54 (close)
Euro/dollar: DOWN at $1.1415 from 1.1463
Pound/dollar: UP at $1.2885 from $1.2844
Dollar/yen: DOWN at 113.17 yen from 113.89
Oil - Brent North Sea: UP 22 cents at $47.74 per barrel
Oil - West Texas Intermediate: UP 45 cents at $45.49 per barrel
source: news.abs-cbn.com
