LONDON — Markets breathed a huge sigh of relief Wednesday after U.S. lawmakers reached a budget agreement that will stop hundreds of billions of dollars in automatic tax increases and spending cuts that risked plunging the world’s biggest economy into recession.

Stocks around the world started 2013 with hefty gains as investors welcomed the vote in the House of Representatives that made sure the U.S. does not go over the so-called “fiscal cliff.” Though longer-term fiscal problems remain and President Barack Obama will likely face more battles with the Republican-dominated House, investors were relieved that the biggest near-term stumbling block to the world economy has been cleared.

“The degree to which the U.S. fiscal cliff was causing investors to repress risk appetite is all too clear on the first trading day of 2013,” said Andrew Wilkinson, chief economic strategist at Miller Tabak & Co.

On Wall Street, the Dow Jones industrial average spiked over 250 points, or 1.9 percent, to 13,362 an hour into the session, while the broader S&P 500 index rose 2.1 percent to 1,455.

In Europe, the FTSE 100 index of leading British shares jumped 2.4 percent to 6,041, its first foray above the 6,000 mark since July 2011. The CAC-40 in France rose 2.4 percent to 3,728 while Germany’s DAX was up 2 percent at 7,760.

Earlier, in Asia, Hong Kong’s Hang Seng index shot up 2.9 percent to close at 23,311.89, its highest finish since June 1, 2011. Australia’s S&P/ASX 200 surged 1.2 percent to close at 4,705.90, its best finish in 19 months while South Korea’s Kospi jumped 1.7 percent to 2,031.10.

The bill that Congress approved calls for higher taxes on income over $400,000 for individuals and $450,000 for couples, a victory for Obama. Earnings above those amounts would be taxed at a rate of 39.6 percent, up from the current 35 percent. It also delays for two months $109 billion worth of across-the-board spending cuts that had been set to start affecting the Pentagon and domestic agencies this week.

If lawmakers had not agreed by the Jan. 1, 2013 deadline on the new budget measures, more than $500 billion in tax increases would have hit the economy in 2013 alone. Government spending worth $109 billion would have been cut from the military and domestic spending programs.

Though fears over an imminent fall off the “fiscal cliff” have eased, investors still have a host of issues to worry about — not least the prospect of more debates over unresolved longer-term U.S. budget issues.

“Cynics will point out that another argument has been booked in for two months’ time, when the debt ceiling comes up for debate, and Republicans will be looking to make progress on the spending cuts that haven’t featured in the New Year deal,” said Chris Beauchamp, market analyst at IG.

Investors will also keep a close watch on any response from the credit rating agencies. After a fight in Congress to raise the debt limit in 2011, Standard & Poor’s lowered the U.S. government’s AAA bond rating, citing the lack of a credible plan to reduce the federal government’s debt. It also voiced its concerns about the “effectiveness, stability and predictability of American policymaking.”

Meanwhile, investors will be monitoring the state of the global economic recovery and Europe’s ongoing battle to contain its 3-year debt crisis.

A better than expected monthly U.S. manufacturing survey from the Institute for Supply Management reinforced the underlying optimism in the markets, especially as investors shift their focus to Friday’s payrolls report for December.

The ISM’s index of manufacturing activity rose to 50.7 in December from 49.5 in the previous month. The rise was slightly more than expected in the markets and took the measure above the 50 threshold that indicates expansion.

“Nothing to dent the positive risk start to the year here,” said Alan Ruskin, an analyst at Deutsche Bank.

While the evidence points to continued economic growth in the U.S., figures elsewhere highlighted the scale of the downturn in the economy of the 17 European Union countries that use the euro.

The manufacturing purchasing managers’ index — a gauge of business activity published by data provider Markit — showed the industrial sector remained mired in recession in December. The index for the eurozone fell to 46.1 from 46.3 the previous month. Anything below 50 indicates a contraction in activity.

How the European economy fares over the coming months will likely hinge on developments in the debt crisis. In the last few months of 2012, tensions eased largely in the wake of the announcement of a new bond-buying plan from the European Central Bank.

That shored up the euro, which eked out further gains Wednesday as investor sentiment was buoyant in the wake of the fiscal cliff deal. When investors have a propensity to take on riskier assets, the dollar often loses ground. The euro was up 0.5 percent at $1.3258.

Oil prices also pushed higher, with the benchmark New York contract up $1.74 at $93.56 a barrel.