Senators voted 89 to 8 to approve the accord around 2am (local time) two hours after a deadline to pass laws halting $US600 billion in tax hikes and spending cuts due to come into force on January 1.
But with Tuesday a holiday, Congress still had time to draw up legislation, approve it and backdate it to avoid the harsh fiscal measures coming into force.
What is the fiscal cliff? Read our explainer
That will need the backing of the House, where many of the Republicans who control the chamber complain that president Barack Obama has shown little interest in cutting government spending to try to reduce the deficit.
Mr Obama praised the Senate for passing the agreement and called on the House to do the same without delay.
Earlier, speaker John Boehner said the House would consider the bill if it passed the Senate, but no decision had been made on whether the House might try to amend it.
"Decisions about whether the House will seek to accept or promptly amend the measure will not be made until House members... have been able to review the legislation," Mr Boehner and other House Republican leaders said in a statement.
The Washington Post says the deal, brokered by vice president Joe Biden, "would let income taxes rise significantly for the first time in more than 20 years, fulfilling Obama's promise to raise taxes on the rich".
The pact would raise taxes on the richest Americans - those earning more than $US450,000 a year - but exempt everyone else, and will put off $US109 billion in budget cuts across the government for two months, top congressional aides told AFP.
The agreement includes a balance of spending cuts and revenue increases to pay for the delay in the automatic spending cuts that would go into effect without a deal by lawmakers.
Of those spending cuts, 50 per cent would come from defence and 50 per cent from non-defence areas, sources told Reuters.
Senate majority leader Harry Reid said that although the Democrats had not got the deal they wanted, they had managed to protect vulnerable Americans.
"I've said all along that our most important priority was to protect middle-class families. This legislation does that," he said.
"Middle-class families will wake up... to the assurance that their taxes wont go up $2,200 each.
"The legislation also protects two million Americans who have lost their jobs during the great recession from losing their unemployment insurance."
The deal would mean a return to Bill Clinton-era tax rates for top earners to 39.6 per cent, starting at a threshold of annual household earnings of $US450,000 and above.
Mr Obama had originally campaigned for tax hikes to kick in for those making $US250,000 and above.