Analysts attributed the gains to strong international economic data, including reports showing eurozone growth accelerated slightly in the second quarter and Chinese manufacturing activity rose in July.
US economic data were mixed, however. A key measure of inflation was flat in June for the second straight month, while the annual rate declined.
Manufacturing activity continued to expand in July, but at a slightly slower pace than in June, according to the Institute for Supply Management.
But US earnings have been strong. Through July 28, companies in the S&P 500 earned 9.1 percent more in the second quarter compared with the year-ago period, according to Factset.
The Dow rose 0.3 percent to 21,963.92, its fifth straight record, after getting to within 10 points of hitting 22,000 for the first time.
"It's a continuation of the bullish momentum," said Karl Haeling of LBBW. "Earnings are good."
London's FTSE 100 rose 0.7 percent, with engines-maker Rolls-Royce shooting over 10 percent higher after exceeding expectations by posting a half-year pre-tax profit of £1.94 billion ($2.57 billion), traders said.
Rolls topped the FTSE with a gain of 10.3 percent to 979 pence.
Energy giant BP, which announced a return to profit, jumped 2.4 percent.
Eurozone stock markets also rose, with Paris up 0.7 percent and Frankfurt jumping 1.1 percent higher as data showed growth in the bloc accelerating slightly in the second quarter to 0.6 percent.
Asian stock markets meanwhile started the month on a high, boosted by strong earnings results and gathering optimism over the global economy.
Equity indexes from Shanghai to Seoul chalked up gains, with confidence fueled by positive Chinese manufacturing data and figures showing South Korean exports surged 20 percent in July from a year earlier.
Sydney's main index recorded gains of almost one percent after Australia's central bank held interest rates at a record low of 1.50 percent.
But the central bank warned that the strengthening "Aussie" was hurting an already soft domestic economy.
Oil prices fell with the WTI contract dropping back below $50 per barrel, having climbed above it on Monday for the first time since May amid optimism that output curbs are cutting back oversupply and reducing stockpiles.
KEY FIGURES AROUND 2050 GMT (4:50 a.m. in Manila)
New York - Dow: UP 0.3 percent at 21,963.92 (close)
New York - S&P 500: UP 0.2 percent to 2,476.35 (close)
New York - Nasdaq: UP 0.2 percent to 6,362.94 (close)
London - FTSE 100: UP 0.7 percent at 7,423.66 points (close)
Frankfurt - DAX 30: UP 1.1 percent at 12,251.29 (close)
Paris - CAC 40: UP 0.7 percent at 5,127.03 (close)
EURO STOXX 50: UP 0.9 percent at 3,478.76
Tokyo - Nikkei 225: UP 0.3 percent at 19,985.79 (close)
Hong Kong - Hang Seng: UP 0.8 percent at 27,540.23 (close)
Shanghai - Composite: UP 0.6 percent at 3,292.64 (close)
Euro/dollar: DOWN at $1.1801 from $1.1840 Monday
Pound/dollar: DOWN at $1.3206 from $1.3208
Dollar/yen: UP at 110.36 yen from 110.25 yen
Oil - Brent North Sea: DOWN 87 cents at $51.78 per barrel
Oil - West Texas Intermediate: DOWN $1.01 at $49.16 per barrel
source: news.abs-cbn.com
