The Dow surged into positive territory for the first time in 2016 on Thursday and the dollar sank a day after the US Federal Reserve's dovish interest rate stance.
European markets were mixed as the stronger euro raised concerns about a negative impact on eurozone exports.
The Dow Jones Industrial Average climbed 0.9 percent as investors cheered the Fed's signal of a more gradual path of interest rate increases. US stocks were further lifted by stronger oil prices and by a big drop in the dollar.
"We're back to game-on," said Mace Blicksilver, director of Marblehead Asset Management. "The Fed took themselves off the table."
But bourses in Frankfurt and Paris slid by 0.9 percent and 0.5 percent, respectively, on worries about the euro's surge against the dollar.
"The rapid appreciation of the euro has the potential to hurt eurozone exporters which have benefited from its weakness," said Oanda analyst Craig Erlam.
Having touched $1.10 last week, the euro shot above $1.13 as investors in the eurozone got their first chance to react to the Fed.
London's FTSE managed a gain of 0.4 percent after the Bank of England kept its key rate on hold at a record low 0.50 percent as expected.
Japan's Nikkei dipped 0.2 percent as the yen strengthened.
- Improving sentiment -
Market sentiment has shifted from the first six weeks of 2016 that saw global stocks retreat on a combination of anxieties over falling oil prices, the weakening China economy and expectations for more Fed tightening.
The Fed on Wednesday trimmed its US growth forecast and projected a slower path of future rate increases in light of global growth worries, seeing only two this year after penciling in four in December.
However many analysts are skeptical the US central bank will be that aggressive.
"It feeds these suspicions that the Fed is canceling the rate cycle slowly but surely," said JPMorgan Chase analyst John Normand.
"The fear of tightening has been hanging over all markets," said Chris Low, chief economist at FTN Financial.
Commodity-linked shares mostly surged, with British-listed miner Anglo American jumping 9.8 percent, French steel company ArcelorMittal rising 10.0 percent and US oil company ConocoPhillips gaining 2.7 percent.
FedEx vaulted 11.8 percent as it reported fiscal third-quarter sales of $12.7 billion, up 8.5 percent from the year-ago period. The package-delivery giant also lifted its 2016 profit forecast range.
The biggest faller in Frankfurt was German airline Lufthansa, whose share price slumped 4.6 percent despite news of soaring 2015 profits.
In Tokyo, Toshiba plunged nearly eight percent on a report that the company is under investigation by US authorities over allegations it hid $1.3 billion in losses at its nuclear power operations.
- Key figures around 2100 GMT -
New York - Dow: UP 0.9 percent at 17,481.49 (close)
New York - S&P 500: UP 0.7 percent at 2,040.59 (close)
New York - Nasdaq: UP 0.2 percent at 4,774.99 (close)
London - FTSE 100: UP 0.4 percent at 6,201.12 points (close)
Frankfurt - DAX 30: DOWN 0.9 percent at 9,892.20 (close)
Paris - CAC 40: DOWN 0.5 percent at 4,442.89 (close)
EURO STOXX 50: DOWN 0.6 percent at 3,043.10 (close)
Tokyo - Nikkei 225: DOWN 0.2 percent at 16,936.38 (close)
Shanghai - composite: UP 1.2 percent at 2,904.83 (close)
Hong Kong - Hang Seng: UP 1.2 percent at 20,503.81 (close)
Euro/dollar: UP at $1.1317 from $1.1226 on Wednesday
Dollar/yen: DOWN at 111.44 yen from 112.57 yen