* Upbeat growth data pushes world stocks higher
* Euro near three-year high
* Oil hits highest since mid 2015 (Updates to U.S. trading open; changes byline, dateline, previously LONDON)
NEW YORK, Jan 4 (Reuters) - Strong data from the world's largest economies helped global shares climb to new heights on Thursday, while the euro hovered near a three-year high and the U.S. dollar fell against major currencies.
MSCI's gauge of stocks across the globe broke a new record, with an advance of 0.79 percent.
On Thursday, the ADP National Employment Report showed that U.S. private employers added 250,000 jobs in December, marking the biggest monthly increase since March.
The Dow Jones Industrial Average rose 153.65 points, or 0.62 percent, to 25,076.33, sailing past the 25,000-mark for the first time. The S&P 500 gained 11.48 points, or 0.42 percent, to 2,724.54 and the Nasdaq Composite added 9.99 points, or 0.14 percent, to 7,075.53, with both indexes hitting fresh highs.
Separately, China's services sector activity hit its highest level in more than three years, manufacturing data from Japan came in strong, and euro zone surveys showed the bloc enjoying its strongest run in nearly seven years.
London's FTSE set a record on Thursday and was up 0.28 percent, while Tokyo's Nikkei - Asia's biggest market - had earlier shot to its highest since 1992 and was up 3.26 percent.
MSCI's broadest index of Asia-Pacific shares outside Japan closed up 0.51 percent, scaling a decade-high peak as a fifth day of gains in China helped emerging market stocks to a six-and-a-half year high.
Those gains come after Wednesday's release of the minutes from the Federal Reserve's mid-December meeting that did little to change a view that it will stick to measured increases in U.S. interest rates.
The minutes showed policymakers expect U.S. President Donald Trump's tax overhaul will boost consumer spending but are still uncertain about the wider impact the stimulus would have on factors such as inflation.
The euro resumed a rally that has taken it near its highest levels in three years, while the U.S. dollar index, which measures the greenback against a basket of major currencies, failed to hold its previous session's gains after upbeat U.S. data and minutes from the Federal Reserve.
The euro rose 0.45 percent to $1.2066, while the dollar index was down 0.27 percent.
The stronger-than-expected U.S. private-sector jobs report briefly helped the dollar pare losses versus the euro and extend gains against the yen. But those moves were shortlived.
"The market quickly faded, the mini-rally in the dollar as the trend gave way to what we have been seeing for the past several weeks, which is dollar weakness," said Sireen Harajli, currency strategist at Mizuho Corporate Bank in New York.
The Japanese yen weakened 0.31 percent versus the greenback at 112.87 per dollar, while Sterling was last trading at $1.3545, up 0.23 percent on the day.
U.S. Treasury yields rose, with two-year yields hitting a more than nine-year peak as upbeat December private hiring data boosted expectations that the Fed would raise interest rates at its March policy meetings.
Benchmark 10-year notes last fell 8/32 in price to yield 2.4743 percent, from 2.445 percent late on Wednesday.
The 30-year bond last fell 14/32 in price to yield 2.8042 percent, from 2.783 percent late on Wednesday.
Oil rose above $68 a barrel to its highest since May 2015 after unrest in Iran sparked concerns about supply risks and with support coming from OPEC-led output cuts and demand-boosting cold weather in the United States.
U.S. crude rose 0.71 percent to $62.07 per barrel and Brent was last at $68.01, up 0.25 percent on the day.
(Additional reporting by Marc Jones, Alex Lawler and Jemima Kelly in London, Gertrude Chavez-Dreyfuss and Richard Leong in New York; Editing by Bernadette Baum)