Early on New Year's Day, the Democrat-dominated Senate passed legislation to block huge tax increases and spending cuts by an overwhelming 89-8.
A vote in the Republican-led House of Representatives is expected later today.
Shortly after the Senate vote, President Barack Obama welcomed the deal, which came after weeks of intense negotiations.
He said: "While neither Democrats nor Republicans got everything they wanted, this agreement is the right thing to do for our country and the House (of Representatives) should pass it without delay."
Mr Obama said the Bill takes a balanced approach to shrinking the US deficit by "investing in (the) middle class" while "asking the wealthy to pay a little more".
The White House-backed legislation prevents middle-class taxes from rising sharply but raises rates on incomes over $400,000 (£245,800) for individuals and $450,000 (£276,000) for couples.
It also blocks spending cuts for two months, extends unemployment benefits for the long-term jobless, prevents a 27% cut in fees for doctors who treat Medicare patients and prevents a spike in milk prices.
A last-minute addition also blocks a $900 (£553) pay rise for members of Congress - those serving in both the Senate and House - from taking effect in March.
Without legislation, economists had warned of a possible new recession and spike in unemployment if the fragile US economy were allowed to fall over the so-called fiscal cliff of tax increases and spending cuts.
With the midnight deadline approaching there was frantic activity in Washington as the Obama administration and politicians spent the final hours of 2012 haggling over long-festering differences.
"It shouldn't have taken this long to come to an agreement, and this shouldn't be the model for how we do things around here," said Senate Republican leader Mitch McConnell, who negotiated the agreement with Vice-President Joe Biden.
Under the deal, spending cuts totalling $24billion (£14.7 billion) over two months at the Defence Department and elsewhere will be deferred.
That will allow the White House and politicians time to regroup before plunging very quickly into a new round of budget brinkmanship certain to revolve around Republican calls to rein in the cost of the Medicare healthcare programme and other government benefit schemes.
As darkness fell on the last day of the year, Mr Obama, Mr Biden and their aides were at work in the White House, and lights still burned in the House of Representatives and Senate.
Democrats complained that Mr Obama had given away too much in agreeing to limit tax increases to incomes over $450,000, far above the $250,000 level he campaigned on. Yet some Republicans recoiled at the prospect of raising taxes at all.
Democratic senators ended up overwhelmingly supporting the measure after being briefed in a closed-door session with Mr Biden.
"The argument is that this is the best that can be done on a bipartisan basis," said Democratic Senator Dianne Feinstein.
Passage of the bill in the Senate sends the measure to the House of Representatives, where Speaker John Boehner refrained from endorsing a package as yet unseen by his famously rebellious rank-and-file.
He said the House would not vote on any Senate-passed measure "until House members - and the American people - have been able to review" it.
House Democratic leader Nancy Pelosi issued a statement saying that once the legislation cleared the Senate "I will present it to the House Democratic caucus".
And while the nominal deadline for action passed at midnight, Mr Obama's signature on legislation by the time a new Congress takes office at noon on January 3 - the likely timetable - would eliminate or minimise any inconvenience for taxpayers.
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