The vote was 285-144, with 87 Republicans voting with 198 Democrats in favor, while 144 Republicans voted against the bill. It came after the Senate voted 81-18 to pass the bill, which President Barack Obama said he will signed as soon as it reaches his desk.
Speaker John Boehner, R-Ohio, urged House Republicans to support the Senate compromise, which would reopen the federal government and keep it open until Jan. 15, and suspend the legal borrowing limit to Feb. 7, turning over negotiations on those issues to a joint committee that must report by mid-December. The deal deal also includes back pay for about 800,000 furloughed federal workers.
Speaking with White House reporters after the Senate vote, Obama thanked "the leaders of both parties for getting us to this point."
"Once this agreement arrives on my desk, I will sign it immediately," he said. "We'll begin reopening our government immediately, and we can begin to lift this cloud of uncertainty and unease from our businesses and from the American people."
The president said he will speak Thursday on "how we can move forward in the remainder of the year and stay focused on the job at hand, because there is a lot of work ahead of us, including our need to earn back the trust of the American people that has been lost over the last few weeks. And we can begin to do that by addressing the real issues that they care about."
After the Senate vote, Sen. Chuck Schumer, D-N.Y., said passage of the bipartisan measure showed "that brinksmanship doesn't work."
He said Democrats held firm against Republican attempts to use the debt limit and the government shutdown to defund the Affordable Care Act, widely known as Obamacare.
"If we gave in this time we'd be back doing the same thing next quarter and the quarter after that and the quarter after that," he said.
Sen. Ted Cruz, R-Texas, a leader of the fight to defund the ACA, said on the Senate floor prior to the vote his opposition to reopening the government and extending the debt limit was based on helping people "who have been hurt by Obamacare." He said the brokered agreement says to those people "you don't have a voice in Washington."
"This is a terrible deal," Cruz said.
He told right-wing radio talk show host Mark Levin Senate Republicans were "bombing our own troops" in the House, and said his effort to defund the Affordable Care Act had achieved "an incredible victory" in the budget fight.
Sen. Jeff Flake, R-Ariz., wrote on his Facebook page there is no way to "spin a Republican victory on the shutdown."
"Many were led to believe that Obamacare could be defunded if Republicans would just stand firm and refuse to pass a continuing resolution," he said. "A continuing resolution was not passed, the shutdown occurred and Obamacare was still funded. That's more of a black eye than a victory, but we'll take our lumps and put it behind us."
The Senate vote came after the White House released a statement saying the Obama administration "strongly supports Senate passage of the amendment in the nature of a substitute to H.R. 2775" and urging the House "to act swiftly to pass the bill in order to protect the full faith and credit of the United States and end the government shutdown."
The Senate vote came after House Speaker John Boehner, R-Ohio, said Republicans would not block the Senate-brokered deal.
Though Boehner promised not to block the deal, he was defiant on the ACA, which Republicans tried to defund by using the shutdown and the debt limit increase as leverage.
"The House has fought with everything it has to convince the president of the United States to engage in bipartisan negotiations aimed at addressing our country's debt and providing fairness for the American people under Obamacare," Boehner said in a statement.
"That fight will continue. But blocking the bipartisan agreement reached today by the members of the Senate will not be a tactic for us. In addition to the risk of default, doing so would open the door for the Democratic majority in Washington to raise taxes again on the American people and undo the spending caps in the 2011 Budget Control Act without replacing them with better spending cuts.
"With our nation's economy still struggling under years of the president's policies, raising taxes is not a viable option. Our drive to stop the train wreck that is the president's healthcare law will continue."
Boehner said Republicans "will rely on aggressive oversight that highlights the law's massive flaws and smart, targeted strikes that split the legislative coalition the president has relied upon to force his healthcare law on the American people."
"The president believes that this [legislation] achieves what's necessary in reopening the government and avoiding default," White House press secretary Jay Carney told reporters.
"He looks forward to Congress acting so he can sign the legislation. ... The president hopes both houses will act swiftly."
From the Senate floor, in announcing the deal, Senate Majority Leader Harry Reid, D-Nev., said the legislation sets up a budget conference committee, with members from both chambers of Congress.
"The eyes of the world have been on Washington all this week," Reid said. "Our country came to the brink of disaster."
Reid added, "This [budget] legislation also funds the government through Jan. 15 and avoids default through Feb. 7."
The majority leader thanked Senate Minority Leader Mitch McConnell, R-Ky., who said Republicans remain committed to repealing the ACA.
The proposal includes no major concessions on the healthcare law. It does require the administration to begin income verification for those applying for insurance subsidies. The act includes that requirement, but the administration had delayed verification for technical reasons.
Reid and McConnell rushed to finish the deal only hours before the midnight deadline to raise the nation's $16.7 trillion debt limit.
The administration had said Thursday was the day when it will be left with only about $30 billion on hand to pay the nation's bills.
Amid the Capitol Hill turmoil, Fitch Ratings put the United States on a "negative ratings watch," warning "political brinkmanship and reduced financing flexibility" raised the risk of default.
The move by the No. 3 credit-rating agency was widely seen as a step toward a potential downgrade of the government's triple-A rating.