"I sought this office to restore the soul of America," Biden said in a prime-time victory speech not far from his Delaware home, "and to make America respected around the world again and to unite us here at home."
Biden crossed the winning threshold of 270 Electoral College votes with a win in Pennsylvania. His victory came after more than three days of uncertainty as election officials sorted through a surge of mail-in votes that delayed processing.
WATCH: Biden pledges to be a president who seeks unity in acceptance speech from Delaware
Trump refused to concede, threatening further legal action on ballot counting. But Biden used his acceptance speech as an olive branch to those who did not vote for him, telling Trump voters that he understood their disappointment but adding, "Let's give each other a chance."
"It's time to put away the harsh rhetoric, to lower the temperature, to see each other again, to listen to each other again, to make progress, we must stop treating our opponents as our enemy," he said. "We are not enemies. We are Americans."
Biden, 77, staked his candidacy less on any distinctive political ideology than on galvanizing a broad coalition of voters around the notion that Trump posed an existential threat to American democracy. The strategy, as well as an appeal to Americans fatigued by Trump's disruptions and wanting a return to a more traditional presidency, proved effective and resulted in pivotal victories in Michigan and Wisconsin as well as Pennsylvania, one-time Democratic bastions that had flipped to Trump in 2016.
SEE ALSO: Joe Biden is set to become the next president of the US, vowing new direction for divided country
Biden's victory was a repudiation of Trump's divisive leadership and the president-elect now inherits a deeply polarized nation grappling with foundational questions of racial justice and economic fairness while in the grips of a virus that has killed more than 236,000 Americans and reshaped the norms of everyday life.
Kamala Harris made history as the first Black woman to become vice president, an achievement that comes as the U.S. faces a reckoning on racial justice. The California senator, who is also the first person of South Asian descent elected to the vice presidency, will become the highest-ranking woman ever to serve in government, four years after Trump defeated Hillary Clinton.
WATCH: Victory speech: VP-elect Kamala Harris says voters have "ushered in a new day for America"
Harris introduced Biden at their evening victory celebration as "a president for all Americans" who would look to bridge a nation riven with partisanship and she nodded to the historic nature of her ascension to the vice presidency.
"Dream with ambition, lead with conviction and see yourselves in a way that others may not simply because they've never seen it before," Harris told Americans. "You chose hope and unity, decency, science and, yes, truth ... you ushered in a new day for America."
After he spoke, the cars at the drive-in rally - a pandemic campaign invention - began to honk their horns and a fireworks display lit up the night sky. Biden was on track to win the national popular vote by more than 4 million, a margin that could grow as ballots continue to be counted.
Biden was born in Scranton and sought to contrast his working-class roots with the affluent Trump's by casting the race as "Scranton versus Park Avenue." It was a familiar theme for Biden, who has long played up his connection to lunch-bucket Scranton and still has friends there.
"Against extraordinary odds, he achieved what he really wanted, his goal," said lifelong friend Tom Bell, a retired insurance agent who grew up in the same neighborhood as Biden.
Biden has long played up the idea that he was Pennsylvania's "third senator" during his decades representing neighboring Delaware. He also campaigned extensively in the state from his home in Delaware.
SEE ALSO: Celebration in Philly after Biden elected president of the United States
Until 1952, Biden lived with his parents and grandparents in a two-story Colonial on a tree-lined street in Green Ridge, an Irish Catholic enclave and one of Scranton's nicest neighborhoods. Biden slept in an attic bedroom with sloped ceilings and a view of West Mountain, scrawling "Joe Biden was here" and "Kilroy was here" on the walls.
The family moved to Delaware in search of greater opportunity, but Biden returned frequently. As a senator, he was a familiar presence in the Philadelphia media market.
Delaware, now the epicenter of the political universe, went into celebration mode after news broke that one of their own was being elected president.
Kamala Harris tweeted a video of her calling Joe Biden after several news organizations declared him the winner of the U.S. presidency.
WATCH: Kamala Harris calls Joe Biden after he becomes apparent president-elect
"I cried. You just don't even know. I'm so tired of the hypocrite that's in the White House," said Carol Riley.
"I was born and raised here. So, to have vice president, now president is just monumental for this little state," added Veronica Renteriamojica.
"Everybody's just excited for this day. We waited for extra days to get here and we're just glad to see it happen," said another Biden.
Trump says he's not giving up.
Departing from longstanding democratic tradition and signaling a potentially turbulent transfer of power, he issued a combative statement saying his campaign would take unspecified legal actions. And he followed up with a bombastic, all-caps tweet in which he falsely declared, "I WON THE ELECTION, GOT 71,000,000 LEGAL VOTES." Twitter immediately flagged it as misleading.
Trump has pointed to delays in processing the vote in some states to allege with no evidence that there was fraud and to argue that his rival was trying to seize power - an extraordinary charge by a sitting president trying to sow doubt about a bedrock democratic process.
Trump is the first incumbent president to lose reelection since Republican George H.W. Bush in 1992.
WATCH: Large crowd gathers in Center City Philadelphia after Joe Biden elected president
He was golfing at his Virginia country club when he lost the race. He stayed out for hours, stopping to congratulate a bride as he left, and his motorcade returned to the White House to a cacophony of shouts, taunts and unfriendly hand gestures.
-- The Associated Press contributed to this report.