By a vote of 257 to 167, the Republican-controlled House of Representatives approved a bill that fulfills President Barack Obama's re-election promise to raise taxes on top earners.
The Senate passed the measure earlier in a rare New Year's Day session and Obama is expected to sign it into law shortly.
The United States will no longer go over a "fiscal cliff" of tax hikes and spending cuts that had been due to come into force on Tuesday but other bruising budget battles lie ahead in the next two months.
It was a reversal for House Republicans, who were in disarray despite winning deep spending cuts in earlier budget fights. But they saw their leverage slip away this time when they were unable to unite behind any alternative to Obama's proposal.
House Speaker John Boehner and other Republican House leaders stayed silent during the debate on the House floor, an unusual move for a major vote.
The deal shatters two decades of Republican anti-tax orthodoxy by raising rates on the wealthiest even as it makes cuts for everybody else permanent.
Lawmakers had struggled to find a way to head off across-the-board tax hikes and spending cuts worth $600 billion that began to take effect at midnight on January 1, a legacy of earlier failed budget deals that is known as the fiscal cliff.
Strictly speaking, the United States went over the cliff in the first minutes of the New Year because Congress failed to act on time. But the bill passed on Tuesday will be backdated.
While many Republicans were uneasy with the tax hikes and wanted more spending cuts, they seemed to realize that the fiscal cliff would begin to damage the economy once financial markets and federal government offices returned to work on Wednesday. Opinion polls show the public would blame Republicans if a deal were to fall apart.
Income tax rates will now rise on families earning more than $450,000 per year and the amount of deductions they can take to lower their tax bill will be limited.
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 $2,000 more taken out of their paychecks annually with the expiration of a temporary payroll tax cut.
The non-partisan Congressional Budget Office said the bill would increase budget deficits by nearly $4 trillion over the coming 10 years, compared to the budget savings that would occur if the extreme measures of the cliff were to kick in.
But the bill would actually save $650 billion during that time period when measured against the tax and spending policies that were in effect on Monday, according to the Committee for a Responsible Federal Budget, an independent group that has pushed for more aggressive deficit savings.
(Additional reporting by Rachelle Younglai, Kim Dixon and David Lawder; Writing by Andy Sullivan; Editing by Alistair Bell and Eric Beech)