The Senate approved a bipartisan agreement early Tuesday morning to let income taxes rise sharply for the first time in two decades, fulfilling President Obama’s promise to raise taxes on the rich and avoiding the worst effects of the “fiscal cliff.” The agreement, brokered by Vice President Biden and Senate Minority Leader Mitch McConnell (R-Ky.), passed 89 to 8 in a highly unusual New Year’s morning vote. It now heads to the House, where leaders have not guaranteed passage but top officials believe it could win passage in the next few days.

The agreement primarily targets taxpayers who earn more than $450,000 per year, raising their rates for wages and investment profits. At the same time, the deal would protect more than 100 million households earning less than $250,000 a year from income tax increases scheduled to take effect Jan. 1.

The deal came together barely three hours before the midnight deadline, after negotiators cleared two final hurdles involving the estate tax and automatic spending cuts set to affect the Pentagon and other federal agencies this week.

Republicans gave in on the spending cuts, known as sequestration, by agreeing to a two-month delay in budget reductions that would be paid for in part with new tax revenue, a condition they had resisted. And the White House made a major concession on the estate tax, agreeing to terms that would permit estates worth as much as $15 million to escape taxation by the end of the decade, Democrats said.

As the deadline for agreement closed in on Monday, Biden rushed to the Capitol to brief Senate Democrats on the deal, as Majority Leader Harry M. Reid (D-Nev.) laid plans for a vote shortly after midnight, when taxes were set to rise for virtually every American.

“I think we’ll get a very good vote tonight,” a beaming Biden said as he emerged from the meeting with Democrats after nearly two hours. “But happy new year and I’ll see you all maybe tomorrow.”

The measure is now at the House, where Speaker John A. Boehner (R-Ohio) pledged to bring it to a vote in the coming days. “Decisions about whether the House will seek to accept or promptly amend the measure will not be made until House members — and the American people — have been able to review the legislation,” Boehner and other GOP leaders said in a written statement.

Senior aides predicted the measure would pass the House with bipartisan support. But Boehner’s decision to delay the vote meant the nation would tumble over the cliff at least briefly.

In addition to dealing with the fiscal crisis, the measure would extend federal farm policies through September, averting an estimated doubling of milk prices. The deal also nixed a set pay raise for members of Congress.

During a midday event at the White House, Obama praised the emerging agreement even though it would raise only about $600 billion over the next decade by White House estimates — far less than the $1.6 trillion the president had initially sought to extract from the nation’s richest households.

The agreement “would further reduce the deficit by asking the wealthiest 2 percent of Americans to pay higher taxes for the first time in two decades. . . . So that’s progress,” Obama said.

“Keep in mind that just last month, Republicans in Congress said they would never agree to raise tax rates on the wealthiest Americans. Obviously, the agreement that’s currently being discussed would raise those rates and raise them permanently,” he said.

Some liberals were fuming about the accord, complaining that Obama had been promising to increase taxes on income over $250,000 a year — a much lower threshold — since he ran for the White House in 2008.

Sen. Tom Harkin (D-Iowa) said: “If you make $250,000 a year, you’re not middle class. You’re in the top 2 percent of income earners in America... No deal is better than a bad deal, and this looks like a very bad deal the way this is shaping up.”

Other Democrats were upset about the administration’s decision to maintain a big exemption for inherited estates that allows those worth as much as $5 million — $10 million for couples — to go untaxed.

Although the White House won an agreement to raise the tax rates on larger estates from 35 percent to 40 percent, Republicans successfully insisted that the exemption should be adjusted annually for inflation, a provision that would increase the exemption amount to $7.5 million for individuals and $15 million for couples by 2020, said Rep. Chris Van Hollen (Md.), the ranking Democrat on the House Budget Committee.

He called the final agreement a “sweetheart giveaway to the wealthiest 7,200 estates in the country.”

Republicans, too, were anxious about the accord, especially in the House, which two weeks ago rejected a proposal that would let taxes rise only on income over $1 million a year. GOP lawmakers — who have not voted for a broad tax increase since 1990 — were particularly incensed about the lack of new spending cuts.

Rep. Patrick T. McHenry (N.C.), a staunch conservative, said he was “gravely disappointed” and that House passage of the measure was not guaranteed.

Under the agreement, the top income tax rate would rise from 35 percent to 39.6 percent for married couples earning more than $450,000 a year and single people earning more than $400,000 a year. Those households also would pay higher rates on investment profits, with rates on dividends and capital gains rising from 15 percent to 20 percent.

Combined with a 3.8 percent surcharge on investment income adopted as part of Obama’s health-care initiative — a tax that also takes effect in January — the top rate on investment income would rise to 23.8 percent for high-income households.

Nor would taxpayers earning less than $450,000 entirely escape. The deal would restore limits on personal exemptions and itemized deductions that existed during the Clinton administration, with those benefits phasing out for couples earning more than $250,000 a year and single people earning more than $200,000.

That would keep Obama’s campaign pledge to raise taxes on the top 2 percent of earners, essentially households over $250,000. A Democrat familiar with the talks said the president hopes to gain additional revenue from those households by seeking to limit their tax breaks when the battle to reduce record deficits continues in the new year.

By extending lower tax rates for nearly all Americans, the deal would leave tax revenue about $3.7 trillion lower than if the rates had reset at higher levels.

In addition to permanently extending tax cuts enacted during the George W. Bush administration for 114 million households, the deal calls for a permanent fix for the alternative minimum tax, which would otherwise hit nearly 30 million taxpayers for the first time when they file their 2012 returns.

It would extend for five years tax credits for college tuition and the working poor, which were enacted as part of Obama’s 2009 economic stimulus package, benefiting 25 million low-income families.

Businesses would see a variety of popular tax breaks extended through 2013, including a credit for research that primarily benefits high-tech companies and an investment write-off that helps manufacturers.

The long-term unemployed could count on receiving emergency benefits for another year, at a cost of about $30 billion.

And doctors would be spared a 27 percent cut in Medicare reimbursements set to take effect in January — although the $30 billion cost of that extension would be covered by cutting other health-care programs.

The last last piece of the puzzle to fall into place was the sequester, which would be delayed until early March under an agreement to raise $12 billion in new tax revenue and $12 billion in fresh savings from the Pentagon and domestic programs.

Most of the deal had been locked down in a phone call between Biden and McConnell shortly before 1 a.m. Monday.

But at 6:30 a.m., McConnell’s phone rang again. The White House was unhappy with a tentative agreement for handling the sequester.

Those cuts were adopted in the summer of 2011 after an epic battle over the federal borrowing limit. At the time, Boehner insisted on identifying spending cuts equal in size to the increase in the debt limit, which was lifted by $2.1 trillion. About half the savings came in the form of limits on agency budgets over the next 10 years. The rest — about $1.2 trillion over the next decade, including interest savings — would begin on Wednesday, striking every federal account evenly, across the board.

With negotiators focused on how to prevent taxes from rising, the sequester had been largely forgotten. Enter Defense Secretary Leon E. Panetta and other senior Pentagon officials, who mounted an intense campaign over the past two days to spare the military, warning lawmakers that 800,000 civilian jobs were at risk.

Suddenly, the sequester was back on the table. The White House at first sought a two-year delay, which would have added more than $200 billion to budget deficits. Republicans demanded new spending cuts and offered $120 billion in options.

As the talks continued, Obama appeared at the White House, demanding in a campaign-style event that any plan to pay for the sequester must be “balanced.”

“That means the revenues have to be part of the equation in turning off the sequester and eliminating these automatic spending cuts,” he said.

The announcement angered Republicans; a top aide to McConnell tweeted that Obama had just “moved the goalpost.”

Soon after, McConnell appeared on the Senate floor to plead for the deal to move forward.

“Let’s take what’s been agreed to and get moving. The president wants this, members of Congress want to protect taxpayers and we can get it done now,” McConnell said. “We must do this.”

Rosalind S. Helderman and Ed O’Keefe contributed to this report.