HIs speech on Saturday in Wilmington, Delaware,, capped off a day of celebrations and impromptu parades nationwide.
"We've won with the most votes ever cast for a presidential ticket ... and we're seeing all over this nation, and in all cities in all parts of the country, indeed across the world, an outpouring of joy."
Biden reached out to those voters who supported President Donald Trump, telling the crowd of supporters: "They are not our enemies. They're Americans."
"This is the time to heal in America," he said.
"I will work to be a president who seeks not to divide but unify. I won't see red states and blue states, I will always see the United States."
Trump has refused to accept the results of the election, and on Saturday the president insisted in a tweet that he had "won this election, by a lot!"
Trump and his campaign have filed lawsuits in a half-dozen closely contested states this week, seeking to create the illusion that the vote was tainted, and that Biden's win is illegitimate. Legal experts have dismissed the suits as meritless.
Biden's only mention of Trump on Saturday was the olive branch he extended to the president's supporters.
"To those who voted for President Trump, I understand your disappointment tonight," he said. "I've lost a couple of elections myself. But now, let's give each other a chance."
"Let this grim era of demonization in America begin to end, here and now."
Biden clinched his victory on Saturday, when the votes tallied over the past four days in Pennsylvania added up to an insurmountable lead for him. The state's 20 electoral college votes pushed his total over the 270-vote threshold needed to win.
Later in the day Saturday, NBC News also projected Biden would win Nevada, adding six Electoral College votes to his column.
Biden said his first priority will be to bring the surging coronavirus pandemic under control. New daily cases have eclipsed 100,000 in recent days. Hospitalizations and deaths are also rising.
"On Monday, I will name a group of leading scientists and experts as Transition Advisors to help take the Biden-Harris COVID plan and convert it into an action blueprint that starts on January 20th, 2021.That plan will be built on a bedrock of science. It will be constructed out of compassion, empathy, and concern," he said.
"I will spare no effort — or commitment — to turn this pandemic around."
Biden was introduced by Vice President-elect Kamala Harris, who made history as the first Black woman and the first Asian American woman to be elected vice president. She touched on these themes in her speech, reaching out to women and girls everywhere.
"While I may be the first woman in this office, I won't be the last," she said. "Because every little girl watching tonight sees that this is a country of possibilities."
"Dream with ambition, lead with conviction, and see yourself in a way that others might not see you, simply because they've never seen it before," she said.
Harris and Biden acknowledged the gravity of the work that lies before them. It won't be easy, they said, but they are ready.
"We have elected a president who represents the best in us," said Harris. "A leader the world will respect and our children can look up to. A commander-in-chief who will respect our troops and keep our country safe. And a president for all Americans."
Biden's speech concluded with a lofty vision of the nation he is poised to lead for the next four years. "We're always looking ahead, ahead to an America that's freer and more just," he said.
"Ahead to an America that creates jobs with dignity and respect. Ahead to an America that cures disease — like cancer and Alzheimer's. Ahead to an America that never leaves anyone behind. Ahead to an America that never gives up, never gives in.
"This is a great nation. And we are a good people."