WASHINGTON — Barack Obama swept to victory as the nation’s first black president Tuesday night in an electoral college landslide that overcame racial barriers as old as America itself. “Change has come,” he told a jubilant hometown Chicago crowd estimated at nearly a quarter-million people.

The son of a black father from Kenya and a white mother from Kansas, the Democratic senator from Illinois sealed his historic triumph by defeating Republican Sen. John McCain in a string of wins in hard-fought battleground states — Ohio, Florida, Iowa and more. He captured Virginia, too, the first candidate of his party in 44 years to do so.

On a night for Democrats to savor, they not only elected Obama the nation’s 44th president but padded their majorities in the House and Senate, and in January will control both the White House and Congress for the first time since 1994.

A survey of voters leaving polling places showed the economy was by far the top Election Day issue. Six in 10 voters said so, and none of the other top issues — energy, Iraq, terrorism and health care — was picked by more than one in 10.

Obama’s election capped a meteoric rise — from mere state senator to president-elect in four years.

Spontaneous celebrations erupted from Atlanta to New York and Philadelphia as word of Obama’s victory spread. A big crowd filled Pennsylvania Avenue in front of the White House.

In his first speech as victor, to an enormous throng at Grant Park in Chicago, Obama catalogued the challenges ahead. “The greatest of a lifetime,” he said, “two wars, a planet in peril, the worst financial crisis in a century.”

He added, “There are many who won’t agree with every decision or policy I make as president, and we know that government can’t solve every problem. But I will always be honest with you about the challenges we face.”

McCain called his former rival to concede defeat — and the end of his own 10-year quest for the White House. “The American people have spoken, and spoken clearly,” McCain told disappointed supporters in Arizona.

President Bush added his congratulations from the White House, where his tenure runs out on Jan. 20. “May God bless whoever wins tonight,” he had told dinner guests earlier.

Obama, in his speech, invoked the words of Lincoln and seemed to echo John F. Kennedy.

“So let us summon a new spirit of patriotism, of service and responsibility where each of us resolves to pitch in and work harder,” he said.

He and his running mate, Sen. Joseph Biden of Delaware, will take their oaths of office as president and vice president on Jan. 20, 2009. McCain remains in the Senate. Sarah Palin, McCain’s running mate, returns to Alaska as governor after a tumultuous debut on the national stage.

He will move into the Oval Office as leader of a country that is almost certainly in recession, and fighting two long wars, one in Iraq, the other in Afghanistan.

The popular vote was close — 51.3 percent to 47.5 percent with 73 percent of all U.S. precincts tallied — but not the count in the Electoral College, where it mattered most.

There, Obama’s audacious decision to contest McCain in states that hadn’t gone Democratic in years paid rich dividends.

After midnight in the East, The Associated Press count showed Obama with 338 electoral votes, well over the 270 needed for victory. McCain had 141 after winning states that comprised the normal Republican base, including Texas and most of the South.

Interviews with voters suggested that almost six in 10 women were backing Obama nationwide, while men leaned his way by a narrow margin. Just over half of whites supported McCain, giving him a slim advantage in a group that Bush carried overwhelmingly in 2004.

The results of the AP survey were based on a preliminary partial sample of nearly 10,000 voters in Election Day polls and in telephone interviews over the past week for early voters.