The Dow has now risen for nine straight sessions, its longest winning run since 1996. Many stock indexes around the world have risen in the slipstream of the Dow's advance to multi-year highs, too.
Investors will later be monitoring weekly U.S. jobless claims figures to see if the recent labor market improvement continues. The consensus in the markets is that claims remained around the 350,000 mark last week.
"There does not appear to be too many doubters that today's weekly jobs numbers will provide even more ammunition for the bulls," said Mike McCudden, head of derivatives at Interactive Investor.
In Europe, the FTSE 100 index of leading British shares was up 0.3 percent at 6,499 while Germany's DAX rose 0.7 percent to 8,027. The CAC-40 in France was 0.6 percent higher at 3,858.
Wall Street was poised for a solid opening with both Dow futures and the broader S&P 500 futures up 0.2 percent. Much of the focus in the markets is on the S&P, which is only around 20 points away from its own all-time high.
Much of the rally in stock markets has been predicated on the assumption that the U.S. Federal Reserve will for the foreseeable future keep interest rates at record lows and continue to pump money into the economy, so-called quantitative easing, or QE.
"It does seem that so long as the Fed is committed to QE, the markets may struggle to find a reason to start heading south," said Fawad Razaqzada, market strategist at GFT Markets.
Earlier in Asia, Japan's Nikkei 225 index rose 1.2 percent to finish at 12,381.19 — its highest close in more than four years — as investors anticipated parliament's approval of Haruhiko Kuroda as chief of the Bank of Japan. Kuroda has been critical of the central bank's policies in the past and is thought to back Prime Minister Shinzo Abe's strategies for seeking to revive Japan's economy by fighting deflation through monetary easing and hefty government spending.
South Korea's Kospi added 0.1 percent to 2,002.13 but stocks in Hong Kong rose 0.3 percent to 22,619.18.
Trading in the currency markets was fairly light, with the euro flat at $1.2953 and the dollar 0.3 percent higher at 96.36 yen.
Oil markets were subdued too, with the price of benchmark New York crude up 15 cents at $92.67 a barrel.