While the passage of the bill to avoid the "fiscal cliff" removed some near-term uncertainty, it did not end the political showdown on the budget. Battles over the sequester, as the automatic spending cuts are known, and the U.S. debt ceiling will come to a head in February.
Marc Chandler, global head of currency strategy at Brown Brothers Harriman in New York, said the financial markets' reaction to the U.S. budget deal was a "a sigh of relief that a recession in the world's largest economy has been averted."
"The coming negotiations about spending cuts and the debt ceiling may be fierce and loud, but also will not produce a dramatic agreement that puts the U.S. on a sustainable fiscal path," he added.
(Read More: Rocky Path Ahead Even as Markets Cheer Fiscal Deal)
Higher-yielding and growth-linked currencies rallied. The Australian dollar rose 0.9 percent to $1.0487 after hitting a two-week high. The New Zealand dollar gained 0.6 percent to $0.8328.
The euro fell 0.3 percent to $1.3171. It had earlier hit a high of $1.3299 on Reuters data, the highest in two weeks and not far from an 8-1/2-month high set on Dec. 19.
"It looks as though someone forgot to tell the euro that it's supposed to go higher after the fiscal cliff agreement," said Matthew Lifson, senior analyst and trader at Cambridge Mercantile Group in Princeton, New Jersey.
The single currency has gained nearly 10 percent since late July when the European Central Bank President Mario Draghi said the ECB would do whatever it takes to save the euro. Strategists say the euro could see renewed pressure if concerns about the weak euro zone economy reemerge.
Euro zone factories sank deeper into recession in December,data showed on Wednesday. Markit's Eurozone Manufacturing Purchasing Managers'Index (PMI) fell to 46.1 from November's 46.2. It has been below the 50 mark that divides growth from contraction since August 2011.
By contrast, data on Wednesday showed U.S. manufacturing ended 2012 on an upswing despite fears about the "fiscal cliff," with factories returning to growth in December after contracting the previous month.
"All the noise (on the fiscal cliff) from the end of the year in the U.S. is over," said Cambridge's Lifson. "It may be time to concentrate on the economies and at present it looks like the European economies are in worse shape than the U.S. economy. Advantage, U.S. dollar? It just may be."
On Friday, the ISM services data and the closely watched U.S. nonfarm payrolls data for December will be released.
Against the yen, the euro rose to 115.99 yen on Reuters data, the strongest since July 2011, and was last up 0.4 percent at 114.89 yen.Option barriers were cited at 116 yen. The dollar rose 0.5 percent versus the yen to 87.07, having touched 87.33 yen earlier, the highest since late July 2010.
The yen has also come under pressure in recent weeks on expectations a new Japanese government led by Prime Minister Shinzo Abe will push the Bank of Japan into more forceful monetary easing.
Speculators' bets against the yen hit more than five-year peaks in December but have eased in the past two weeks. Some strategists warned of a potential yen rebound after the next BOJ meeting on Jan. 21-22. (Read More: Betting on Yen to Fall Further in 2013? Think Again)
In the options market, one-month dollar/yen implied volatility touched an 8-1/2 month high of 9.2 on Wednesday according to Thomson Reuters data as demand to hedge against further yen weakness gathered pace. It was last at 8.65 vols, some way off the mid-December low of 7.1.