“This is the Civil Rights Act of the 21st century,” said Representative James E. Clyburn of South Carolina, the No. 3 Democrat in the House.

Mr. Obama celebrated the House action in remarks at the White House.

“We pushed back on the undue influence of special interests,” Mr. Obama said. “We didn’t give in to mistrust or to cynicism or to fear. Instead, we proved that we are still a people capable of doing big things.”

“This isn’t radical reform,” he added, “but it is major reform.”

After a year of combat and weeks of legislative brinksmanship, House Democrats and the White House clinched their victory only hours before the voting started on Sunday. They agreed to a deal with opponents of abortion rights within their party to reiterate in an executive order that federal money provided by the bill could not be used for abortions, securing for Democrats the final handful of votes they needed to assure passage.

Winding up the debate, Speaker Nancy Pelosi said: “After a year of debate and hearing the calls of millions of Americans, we have come to this historic moment. Today we have the opportunity to complete the great unfinished business of our society and pass health insurance reform for all Americans that is a right and not a privilege.”

The House Republican leader, Representative John A. Boehner of Ohio, said lawmakers were defying the wishes of their constituents. “The American people are angry,” Mr. Boehner said. “This body moves forward against their will. Shame on us.”

Republicans said the plan would saddle the nation with unaffordable levels of debt, leave states with expensive new obligations, weaken Medicare and give the government a huge new role in the health care system.

The debate on the legislation set up a bitter midterm campaign season, with Republicans promising an effort to repeal the legislation, challenge its constitutionality or block its provisions in the states.

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Representative Paul D. Ryan, Republican of Wisconsin, denounced the bill as “a fiscal Frankenstein.” Representative Lincoln Diaz-Balart, Republican of Florida, called it “a decisive step in the weakening of the United States.” Representative Virginia Foxx, Republican of North Carolina, said it was “one of the most offensive pieces of social engineering legislation in the history of the United States.”

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But Representative Marcy Kaptur, Democrat of Ohio, said the bill heralded “a new day in America.” Representative Doris Matsui, Democrat of California, said it would “improve the quality of life for millions of American families.”

The health care bill would require most Americans to have health insurance, would add 16 million people to the Medicaid rolls and would subsidize private coverage for low- and middle-income people, at a cost to the government of $938 billion over 10 years, the Congressional Budget Office said.

The bill would require many employers to offer coverage to employees or pay a penalty. Each state would set up a marketplace, or exchange, where consumers without such coverage could shop for insurance meeting federal standards.

The budget office estimates that the bill would provide coverage to 32 million uninsured people, but still leave 23 million uninsured in 2019. One-third of those remaining uninsured would be illegal immigrants.

The new costs, according to the budget office, would be more than offset by savings in Medicare and by new taxes and fees, including a tax on high-cost employer-sponsored health plans and a tax on the investment income of the most affluent Americans.

Cost estimates by the budget office, showing that the bill would reduce federal budget deficits by $143 billion in the next 10 years, persuaded some fiscally conservative Democrats to vote for the bill.

Democrats said Americans would embrace the bill when they saw its benefits, including some provisions that take effect later this year.

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Health insurers, for example, could not deny coverage to children with medical problems or suddenly drop coverage for people who become ill. Insurers must allow children to stay on their parents’ policies until they turn 26. Small businesses could obtain tax credits to help them buy insurance.

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The Democratic effort to secure the 216 votes needed for passage of the legislation came together only after last-minute negotiations involving the White House, the House leadership and a group of Democratic opponents of abortion rights, led by Representative Bart Stupak of Michigan. On Sunday afternoon, members of the group announced that they would support the legislation after Mr. Obama promised to issue an executive order to “ensure that federal funds are not used for abortion services.”

Mr. Stupak described the order as a significant guarantee that would “protect the sanctity of life in health care reform.” But supporters of abortion rights — and some opponents — said the order merely reaffirmed what was in the bill.

The vote to pass the Senate version of the bill means that it will become the law of the land as soon as Mr. Obama signs it, regardless of when — or even whether — the Senate acts on the package of changes the House also passed.

The Senate majority leader, Harry Reid of Nevada, has promised to take up the package of changes in short order, and he has said he has the votes to pass it. The Senate will consider it under a parliamentary maneuver that will allow the Democrats to pass it with a simple majority, averting the threat of a Republican filibuster.

Indeed, Senate Republicans were quickly faced with a need to recalibrate their message from one aimed at stopping the legislation to one focused on winning back a sufficient number of seats in Congress to repeal it.

Mr. Obama, in his remarks shortly before midnight in the East Room, urged the Senate to complete the final pieces of the legislation. “Some have predicted another siege of parliamentary maneuvering in order to delay it,” he said. “I hope that’s not the case.”

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He continued, “It’s time to bring this debate to a close and begin the hard work of implementing this reform properly on behalf of the American people.”

Mr. Obama watched the roll call with Vice President Joseph R. Biden Jr. in the Roosevelt Room in the White House.

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The House galleries were full, and the floor was unusually crowded, for the historic debate on health care.

Working together, Mr. Obama and Ms. Pelosi revived the legislation when it appeared dead after Democrats lost their 60th vote in the Senate and with it their ability to shut off Republican filibusters.

Republicans said they would use the outcome to bludgeon Democrats in this year’s Congressional elections. The White House is planning an intensive effort to convince people of the bill’s benefits. But if Democrats suffer substantial losses in November, Mr. Obama could be stymied on other issues.

The campaign for a health care overhaul began as a way to help the uninsured. But it gained momentum when middle-class families with health insurance flooded Congress with their grievances. They complained of soaring premiums. They said their insurance had been canceled when they got sick.

“It’s not just the uninsured,” said Representative Jim McGovern, Democrat of Massachusetts. “We also have to worry about people with insurance who find, for crazy reasons, that they are somehow going to be denied coverage.”

In the end, groups like the United States Chamber of Commerce and the National Federation of Independent Business tried to stop the bill, saying it would increase the cost of doing business. But other groups, including the American Medical Association and AARP, backed it, as did the pharmaceutical industry.

Lawmakers agreed that Sunday’s debate was historic, but they were poles apart in assessing the legislation.

Representative Rodney Alexander, Republican of Louisiana, said, “You cannot expect to expand coverage to millions of individuals and to curb costs at the same time.”

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Republicans said the picture painted by the budget office was too rosy, because the new taxes and fees would start immediately, while the major costs would not show up for four years.

Moreover, Republicans said Democrats would pay a price for defying public opinion on the bill.

“Are you so arrogant that you know what’s best for the American people?” Representative Paul Broun, Republican of Georgia, asked the Democrats. “Are you so ignorant to be oblivious to the wishes of the American people?”

Lawmakers spoke with deep conviction in explaining their votes.

“Health care is not only a civil right, it’s a moral issue,” said Representative Patrick J. Kennedy, Democrat of Rhode Island, who invoked the memory of his father, Senator Edward M. Kennedy, a Massachusetts Democrat and a lifelong champion of health care for all.

After the legislation passed, Mr. Obama sought to place the day in perspective.

“In the end what this day represents is another stone firmly laid in the foundation of the American dream,” the president said. “Tonight, we answered the call of history as so many generations of Americans have before us. When faced with crisis, we did not shrink from our challenges. We overcame them. We did not avoid our responsibilities, we embraced it. We did not fear our future, we shaped it.”