The Dow is up 1,052.83 points, or 3.7%.
Asian shares were mostly higher Tuesday, encouraged by news on the development of coronavirus vaccines and more assurance for a transition of power in the U.S.to President-elect Joe Biden.
Reports that Biden plans to nominate former Federal Reserve Chair Janet Yellen to become the next Treasury Secretary further boosted United States stocks on expectations she would pursue more conventional policies than the outgoing Steven Mnuchin.
In the bond markets, the yield on the 10-year benchmark rose slightly to 0.87% as it did on most European government bonds.
France's CAC 40 added 1.0% in early trading to 5,547.48, while Germany's DAX rose 0.6% to 13,209.59.
"Investors continue to embrace and see the optimism in the development of vaccines, providing light at the end of the tunnel and multiple choices on how to get there", said Adam Taback, chief investment officer for Wells Fargo Private Bank.
President Trump took credit for the Dow Jones Industrial Average hitting a record 30,000 points on Tuesday, calling it "a sacred number" reached through his administration's policies, including the development of vaccines for COVID-19. The Nasdaq Composite Index was up 25.66 points, or 0.22 percent, to 11,880.63.
The Russell 2000 index of smaller stocks picked up 32.96 points, or 1.8%, to 1,818.30. Cruise line operator Carnival rose 4.7% and hotel company Marriott International gained 3.2%.
On Monday, AstraZeneca joined Moderna, Pfizer and its German partner BioNTech in unveiling upbeat data about the effectiveness of its covid-19 vaccine candidate.
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"This means we have a vaccine for the world", said Andrew Pollard, director of the Oxford University vaccine group that developed the drug.
For the week ending Friday, the Dow declined 0.7 percent, the S&P 500 fell 0.8 percent, and the Nasdaq climbed 0.2 percent, amid coronavirus worries.
Bitcoin rose over 5% and has $20,000 in sight, with traders expecting volatility ahead due partly to Thursday's Thanksgiving holiday in US markets.
Last week, Pfizer and Moderna both reported study results showing their vaccines were nearly 95 per cent effective.
Volume on US exchanges was 12.10 billion shares, compared with the 10.87 billion average for the full session over the last 20 trading days.
With the vaccine news and dollar index, which tracks the dollar against a basket of six major rivals, down to 92.097, commodity markets were still bullish, with traders optimistic about a recovery in crude demand pushing oil higher.
Spot gold fell 0.5% to $1,825.99 per ounce by 0545 GMT, having earlier slid to its lowest since July 21 at $1,820.45. Brent crude, the worldwide standard, gained 39 cents to $46.45 a barrel. The euro cost $1.1843, down from $1.1905.
The Japanese yen weakened 0.07% versus the greenback at 104.62 per dollar, while Britain's pound was last trading at $1.3338, up 0.11% on the day.
