Once that has been done - and the process could still be derailed by last-minute changes of heart among senators - Mr Obama will be able to sign the measure into law.
"We are now finally poised to deliver on the promise of real, meaningful health insurance reform," the president said in a news conference following the Senate vote.
"With today's vote, we are now incredibly close to making health insurance reform a reality in this country."
The Senate bill was adopted by 60 votes to 39, with senators voting along party lines.
Fifty-eight Democrats and two independents backed the legislation, while Republicans voted unanimously against it.
"This is a victory for the American people," Democratic Senate Majority Leader Harry Reid said after the vote.
"Every step of this long process has been an enormous undertaking," Mr Reid added.
Adam Brookes, BBC Washington correspondent
Senators made their way through the icy Washington dawn to Capitol Hill and by about 07:30 local time it was all over. Every Democrat voted in favour and every Republican voted against the healthcare reform bill. This is President Obama's signature policy.
Healthcare reform has dominated American politics all year and it has poisoned the political atmosphere in Washington. Even many of the presidents' own Democratic party were unsure about the bill, its cost and its implications. It fell to Harry Reid, the quietly spoken senator from Nevada, who leads the Democrats in the Senate, to build a tottering consensus among worried Democrats.
Now exhausted senators can leave for their home states and for Christmas. A jubilant President Obama left for holidays in Hawaii. Today's vote was healthcare reform's biggest hurdle, and Mr Obama's presidency has a new momentum today.
Top Republican Senator Mitch McConnell told reporters: "The fight is long from over.
"My colleagues and I will work to stop this bill from becoming law."
The bill's passage in an early morning vote on Christmas Eve follows months of political wrangling and 24 days of debate in the Senate chamber.
Opposition Republicans say the legislation is expensive, authoritarian and a threat to civil liberties and accuse the Democrats of rushing it through.
The BBC's Adam Brookes in Washington says the passage of the Senate bill is an extraordinary political achievement for Mr Obama and will give him a much-needed boost.
But, our correspondent says, the battle is not quite over yet. Congress still has to merge two different bills and vote on them all over again - and on a bill as complex as this, the wheels could still come off.
Healthcare reform has been the key domestic policy of Mr Obama's administration but finalising the details of the proposed bills has been a lengthy and complex process.
I suspect it is all over bar the shouting, but there will be an awful lot of shouting before we're done
On Wednesday, the bill passed the last of three procedural votes in the Senate, with Democrats collecting the 60 votes needed to bring an end to Republican delaying tactics and vote on the final bill.
Under the Senate bill, most Americans would have to have health insurance.
Private insurers would be banned from refusing to provide insurance because applicants had pre-existing medical conditions.
The House version, passed in November, still includes a public option and also differs on how to pay for the reform.
Obama welcomes passing of healthcare bill
The non-partisan Congressional Budget Office estimates that efficiency savings made as a result of the Senate healthcare reform bill will cut the federal deficit by $132bn (£83bn) over 10 years, but critics say the predicted savings may never materialise.
As a nation, the US spent some $2.2tn (£1.36tn) on healthcare in 2007. That amounts to 16.2% of GDP, nearly twice the average of other rich, industrialised countries.
As costs have spiralled, millions of Americans have found themselves unable to afford health insurance and the cost to the government of providing care for the poor and elderly has risen hugely.
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