That man, Mr Bush, 54, must now quickly put together the framework of an administration in little more than a month. He will be inaugurated on 20 January 2001.
He said he had called Republican George W Bush and "congratulated him on becoming the 43rd president of the United States".
In a humourous reference to the events of election night, when he retracted such a call to Mr Bush, he said he had "promised I wouldn't call him back this time".
Mr Gore offered to meet Mr Bush "as soon as possible". Aides said they would meet in Washington next Tuesday.
After five weeks of bitterly partisan legal wrangling, Mr Gore's fate was sealed by a US Supreme Court decision handed down on Tuesday night.
The complicated and divided ruling - which included separate opinions from six of the court's nine judges - essentially said that time had run out for recounts in the critical state of Florida.
Battle for recounts
Mr Gore, a Democrat, criticised the Supreme Court decision in his concession speech, but said he would not challenge it.
"While I strongly disagree with the court's decision, I accept it," he said.
Mr Gore had fought more than a month of courtroom battles to demand hand recounts in several crucial Florida counties in an effort to overturn Mr Bush's tiny lead in Florida.
Twice, Florida's highest court ruled in his favour, and twice the Supreme Court in Washington overturned those decisions.
The Supreme Court ruling on Tuesday meant that Mr Bush preserved his majority of less than 1,000 votes out of six million cast in the state, giving him Florida's 25 electoral votes.
With Florida in the Republican camp, Mr Bush has 271 electoral votes - one more than he needed to win the race - to Mr Gore's 267.
Unity call
As is traditional in concession speeches, Mr Gore urged Americans to unite behind the man who defeated him.
"We put country before party", Mr Gore said of Americans.
He quoted Stephen A Douglas, who lost to Abraham Lincoln in 1860, as saying that after an election, "partisan feeling must yield to patriotism".
Thanking everyone who had worked on his campaign, Mr Gore said: "I particularly urge all who stood with us to stand behind our next president."
Time pressure
That man, Mr Bush, 54, must now quickly put together the framework of an administration in little more than a month. He will be inaugurated on 20 January 2001.
His Vice-President-elect, Dick Cheney, has been working to prepare the transition, but there is little chance a full team will be in place by Inauguration Day.
That is not unusual. When Bill Clinton came into office in 1993, it took him more than a year to fill all the positions a president has to appoint.
Bitter blow
Against expectations, Mr Gore actually used the word "concession" in his speech, saying "I offer my concession".
Admitting defeat must have been a particularly bitter pill for Mr Gore, who actually won the popular vote nationwide. He lost the White House because it is the Electoral College, which operates state by state, that formally selects the president.
And with nearly 50 million ballots in his favour, Mr Gore took more popular votes than Bill Clinton in 1992 and 1996, and more than George Bush - the current president-elect's father - in 1988.
Mr Gore, 52, is the first candidate since Grover Cleveland in 1888 to win the popular vote but lose in the Electoral College.
But perhaps he can take comfort from history. In 1892, President Cleveland became the only man ever to recapture the White House after losing four years before.