Mr Biden has promised to unify -- and not divide -- and has thanked in particular the African-American voters, who placed their trust in him.
He also reached out to Mr Trump's supporters and urged all Americans to "put away the harsh rhetoric" and stop treating people with opposing political views as enemies.
The nation's first female vice president-elect, Kamala Harris, told voters while she may be the first woman in the role, she won't be the last.
Ms Harris is also the first African-American and the first South Asian to be elected Vice President of the United States.
And to the children of our country, regardless of your gender, our country has sent you a clear message: dream with ambition. Lead with conviction and see yourselves in a way that others may not, simply because they have never seen it before. But know that we will applaud you every step of the way.
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