Videos posted to social media sites show cars honking and people cheering and banging pots and pans in cities from New York to Washington, D.C., Chicago and Los Angeles.
While many were wearing masks, they temporarily suspended social distancing even as the country hit a record high in COVID-19 cases for the third consecutive day.
"I am honored and humbled by the trust the American people have placed in me and in Vice President-elect Harris," Biden said in a statement Saturday. "In the face of unprecedented obstacles, a record number of Americans voted, proving once again, that democracy beats deep in the heart of America."
Biden, who campaigned on the promise of uniting a divided nation, urged Americans to "put the anger and the harsh rhetoric behind us" to deal with the country's challenges. "There’s nothing we can’t do, if we do it together."
The Trump campaign, meanwhile, pushed back on the news Saturday, saying in a statement that "Joe Biden is rushing to falsely pose as the winner" and that the election "is far from over."
"Joe Biden has not been certified as the winner of any states, let alone any of the highly contested states headed for mandatory recounts, or states where our campaign has valid and legitimate legal challenges that could determine the ultimate victor," the campaign said. "Legal votes decide who is president, not the news media."
The statement added that on Monday the Trump campaign will begin prosecuting its "case in court to ensure election laws are fully upheld and the rightful winner is seated."