Brown has promised to use his position as the 41st Republican vote to kill off the healthcare changes pushed forward by President Barack Obama.
Martha Coakley, the Democratic Party candidate, conceded defeat on Tuesday.
Reacting to the election upset, Obama urged legislators to come to a quick agreement on core elements of healthcare plan, indicating that he might support a scaled-back overhaul.
"I would advise that we try to move quickly to coalesce around those elements in the package that people agree on," he said in an interview to ABC News on Wednesday.
"We know that we need insurance reform," Obama said. "The health insurance companies are taking advantage of people. We know that we have to have some form of cost containment because if we don't, then our budgets are going to blow up."
|Coakley's defeat raises the spectre of large Democratic losses in mid-term polls [Reuters]
By contrast, Brown told supporters during a victory speech on Tuesday in Boston: "Tonight, the independent voice of Massachusetts has spoken.
"People don't want this trillion-dollar healthcare plan that is being forced on the American people."
Obama acknowledged in the ABC interview that voter anger helped carry Brown to victory, but said: "People are angry, they are frustrated. Not just because of what's happened in the last year or two years, but what's happened over the last eight years."
Massachusetts last elected a Republican to the senate in 1972, but the weak economy and doubts about Obama's healthcare overhaul appeared to have moved some voters to abandon party loyalties.
More broadly, the election upset has raised the spectre of large losses for Democrats in mid-term congressional elections in November.
'Very real anger'
Explaining the significance of the development, Al Jazeera's John Terret, in Washington DC, said: "It's important to understand that Obama is seen differently here in the US compared to how he is seen overseas.
"Looking in from overseas, he is erudite, articulate and professorial, a man concerned with many of the world's problems that perhaps the previous administration was not, and the world welcomes that," he said.
But in the US, our correspondent said, there is "very real anger at the rising level of joblessness and the cost of the healthcare reform being pushed through the congress. Americans are also irritated with national security issues as embodied by the failed Christmas day airliner attack."
Terret said Obama's "own base is angry about sending more troops to Afghanistan.
"Blacks, for example, are irritated that he doesn't take about race issues more, Latinos are concerned that there hasn't been the promised immigration reform and, of course, the Guantanamo Bay [prison] is still open.
"It's all this that Scott Brown tapped into while the Democratic Party candidate was aloof and distant."
Mitch McConnell, the senate Republican leader, said that Brown's victory was a clear sign that Americans had rejected Obama's healthcare proposals.
"They don't want this bill and want Washington to listen to them," he said.
|Massachusetts last elected a Republican to the senate way back in 1972 [GALLO/GETTY]
However, Harry Reid, the Democratic senate majority leader, said that politicians would continue to work towards healthcare reform.
"While Senator-elect Brown's victory changes the political math in the senate, we remain committed to strengthening our economy, creating good paying jobs and ensuring all Americans can access affordable health care," he said.
"We hope that Scott Brown will join us in these efforts."
Toby Chaudhuri, a Democrat strategist, told Al Jazeera: "Its a stunning victory and there is no question that Scott Brown fought a very clever campaign.
"There is a very clear message for the Democrats and that is that they have to wake up," he said.
"There will be a lot of debate here in Washington about what this means, not only for healthcare reform but also for Obama's administration."