In remarks at the White House, Obama rejected arguments by Republican opponents of the bill that it will increase the federal deficit.
"That argument that opponents are making against this bill does not hold water," Obama said.
The nonpartisan Congressional Budget Office says the Senate bill will reduce the deficit by $132 billion in the first 10 years, Obama said.
The Senate will hold more procedural votes on the health care bill this week, with a final vote scheduled for Christmas Eve. If the bill passes, as expected, the Senate version would then be merged in a conference committee with a House health care bill passed last month.
Both chambers would then have to approve the final measure before sending it to Obama to be signed into law.
The Senate vote to end debate was on strictly partisan lines, with all 60 members of the Democratic caucus uniting to overcome a filibuster attempt by the 40 Senate Republicans.
It occurred in a rare overnight session, with voting taking place at 1 a.m. Monday, in order to make it possible for the chamber's final vote to occur before the upcoming Christmas recess.
Obama said the step brought the nation closer to health care reform that would make "a tremendous difference" to Americans by lowering health care costs and eliminating controversial practices by insurance companies to deny coverage for pre-existing conditions or exceeding benefit caps.
The bill also would keep the government-run Medicare program solvent for nearly a decade longer than current projections, and help reduce the "inexorable and unsustainable rise" in health care costs.
The vote left Obama on the cusp of claiming victory on his top domestic priority and enacting the biggest expansion of federal health care guarantees since the enactment of Medicare and Medicaid over four decades ago.
"Today, the Senate took another historic step toward our goal of delivering access to quality, affordable health care to all Americans," Senate Majority Leader Harry Reid, D-Nevada, said in a statement.
The bill will help "promote choice and competition to drive down skyrocketing health care costs for families ... all across America."
Republicans ripped the majority for passing the measure in the middle of the night and accused Democrats of ramming the bill through despite growing public opposition.
"Make no mistake: If the people who wrote this bill were proud of it, they wouldn't be forcing this vote in the dead of night," argued Senate Minority Leader Mitch McConnell, R-Kentucky.
"Mark my words: this legislation will reshape our nation. And Americans have already issued their verdict. They don't want it. They don't like this bill, and they don't like lawmakers playing games with their health care to secure the votes they need to pass it."
The unusual timing of the vote was a consequence of Senate rules, Democrats' determination to pass the bill before adjourning for the holidays, and the GOP's willingness to use every possible legislative tactic to slow the bill's progress.
Unanimous Republican opposition has forced Reid to win the support of all 60 members of his traditionally fractious Democratic caucus. Compromises made to win the backing of more conservative members, such as Nebraska Sen. Ben Nelson and Connecticut Sen. Joe Lieberman, have enraged many liberal Democrats and threatened to undermine support for the bill.
Liberal Democrats are particularly upset with Reid's decision to abandon a government-run public health insurance option and an expansion of Medicare to Americans as young as age 55 -- ideas strongly opposed by Lieberman and other centrists.
Top Democrats, however, argue that the Senate bill as written would still constitute a positive change of historic proportions. The legislation, according to the nonpartisan Congressional Budget Office, would extend health insurance coverage to over 30 million Americans while reducing the federal deficit by $132 billion over the next decade.
The deficit would drop by another $1.3 trillion between the years 2019 and 2029, the CBO said.
Democratic leaders in the House and Senate have now reached agreement on a broad range of changes that could affect every American's coverage.
Among other things, they have agreed to subsidize insurance for a family of four making up to about $88,000 annually, or 400 percent of the federal poverty level.
They have also agreed to create health insurance exchanges designed to make it easier for small businesses, the self-employed and the unemployed to pool resources and purchase less expensive coverage. Both the House plan and the Senate bill would eventually limit total out-of-pocket expenses and prevent insurance companies from denying coverage for pre-existing conditions.
Insurers would also be barred from charging higher premiums based on a person's gender or medical history. Medicaid would be significantly expanded under both proposals.
There are, however, major differences between the Senate measure and the more expansive -- hence expensive -- House bill.
One of the biggest divides is over how to pay for the plans. The House package is financed through a combination of a tax surcharge on wealthy Americans and new Medicare spending reductions. Individuals with annual incomes over $500,000 and families earning more than $1 million would face a 5.4 percent income tax surcharge.
The Senate bill also cuts Medicare by roughly $500 billion. It does not include a tax surcharge on the wealthy, however. It would instead impose a 40 percent tax on so-called "Cadillac" health plans.
Proponents of the tax on high-end plans argue it's one of the most effective ways to curb medical inflation. House Democrats are adamantly opposed to taxing such policies, arguing that such a move would hurt union members who traded higher salaries for more generous benefits.
Another key sticking point is the dispute over a public option. The House plan includes a public option; the more conservative Senate plan would instead create new nonprofit private plans overseen by the federal government.
Under both plans, individuals would be required to purchase coverage. But the House bill includes more stringent penalties for most of those who fail to comply. Both versions include a hardship exemption for poorer Americans.
Employers face a much stricter mandate under the House legislation, which would require companies with a payroll of more than $500,000 to provide insurance or pay a penalty of up to 8 percent of their payroll.
The Senate bill would require any company with more than 50 employees to pay a fee of up to $750 per worker if any of its employees relies on government subsidies to purchase coverage.
Abortion has also been a sticking point for both chambers. A late compromise with conservatives in the House led to the adoption of an amendment banning most abortion coverage from the public option.
It would also prohibit abortion coverage in private policies available in the exchange to people receiving federal subsidies.
Senate provisions, made more conservative than initially drafted in order to satisfy Nelson, would allow states to choose whether to ban abortion coverage in plans offered in the exchanges. Individuals purchasing plans through the exchanges would have to pay for abortion coverage out of their own funds.
Many observers expect the final bill will conform largely to the measure now moving through the Senate.
"Reid had to make a lot of concessions to get his entire caucus behind the Senate bill," said CNN deputy political director Paul Steinhauser.
"He can't afford to a lose a single vote. Every Democratic senator has the power to kill this bill, and that fact gives Senate negotiators tremendous leverage in their negotiations with the House."
Nelson told CNN's "State of the Union" on Sunday that he would withdraw his support if the final bill gets changed too much from the Senate version under consideration.
Among other things, Nelson had a provision added to the bill requiring the federal government to cover Nebraska's costs for expanded Medicaid coverage after 2016. No other state is currently slated to receive such a benefit.