The agreement, approved by the Republican-led House of Representatives after a bitter political struggle, has been hailed a victory for Mr Obama, who had won re-election on a promise to address budget woes in part by raising taxes on the wealthiest Americans.
But it set the stage for a series of political showdowns over the next two months on spending cuts and on raising the nation's limit on borrowing.
News of the agreement was greeted by a stock market surge as the deal fended off immediate austerity measures.
But Republicans, angry the deal did little to curb the federal deficit, promised to use the debt ceiling debate to secure deep spending cuts in the near future.
Republican Senator Pat Toomey of Pennsylvania said: "Our opportunity here is on the debt ceiling. We Republicans need to be willing to tolerate a temporary, partial government shutdown, which is what that could mean."
Republicans, who admitted they had lost the fiscal cliff fight by agreeing to raise taxes on the wealthy without gaining much in return, vowed the next deal would have to include significant cuts in government benefit programmes like Medicare and Medicaid health care for retirees and the poor, which are widely acknowledged as the biggest drivers of federal debt.
Republican Senator Bob Corker of Tennessee said: "This is going to be much uglier to me than the tax issue ... this is going to be about entitlement reform. This is the debate that's going to be far more serious.
"Hopefully, now we have this other piece behind us, we'll deal in a real way with the kinds of things our nation needs to face."
Following the announcement of the interim agreement, Mr Obama urged "a little less drama" when the Congress and White House next address thorny fiscal issues such as the government's rapidly mounting $16 trillion debt load.
After the House of Representatives passed the bill by 257 votes to 167, Mr Obama said the measures were "just one step in the broader effort to strengthen the economy".
Speaking before returning to Hawaii for his interrupted Christmas holiday, Mr Obama said that in signing the law, he was fulfilling a campaign pledge.
"I will sign a law that raises taxes on the wealthiest 2% of Americans ... while preventing a middle-class tax hike," he said.
The breakthrough came late on Tuesday night when dozens of Republicans in the House of Representatives buckled and backed a bill passed by the Democrat-controlled Senate that hiked taxes on households earning more than $450,000 (£276,800) annually.
Low temporary rates that have been in place for the past decade will be made permanent for less-affluent taxpayers, along with a range of targeted tax breaks put in place to fight the 2009 economic downturn.
However, workers will see up to $2000 (£1230) more taken out of their paychecks annually with the expiration of a temporary payroll tax cut. Spending cuts of $109 billion (£67bn) in military and domestic programmes were delayed only for two months.
Economists had warned the fiscal cliff of across-the-board tax hikes and spending cuts would have punched a $600bn (£369bn) hole in the economy this year and threatened to send the country back into recession.
House Republicans had mounted a late effort to add hundreds of billions of dollars in spending cuts to the package and spark a confrontation with the Senate, but it failed.
In the end, they reluctantly approved the Senate bill by a bipartisan vote of 257 to 167.
"We are ensuring that taxes aren't increased on 99% of our fellow Americans," said Republican Representative David Dreier.
Mr Boehner backed the bill but most House Republicans, including his top lieutenants, voted against it. The speaker had sought to negotiate a "grand bargain" with Mr Obama to overhaul the US tax code and rein in health and retirement programmes that will balloon in coming decades as the population ages.