The former California attorney general has been urging police reform amid nationwide anti-racism protests.
Mr Biden will face President Donald Trump in the election on 3 November.
At a White House news conference on Tuesday, Mr Trump, a Republican, described Ms Harris as "my number one draft pick".
Ms Harris will debate Mr Trump's running mate, Vice-President Mike Pence, on 7 October in Salt Lake City, Utah.
Only two other women have been nominated as vice-presidenti
A woman of colour has never been appointed to a presidential ticket by either of the two main American political parties. No woman has won the US presidency either.
Kamala Devi Harris was born on October 20, 1964, in Oakland, California. Her mother, Shyamala Gopalan, was a breast-cancer scientist who had emigrated from Tamil Nadu, India in 1960 to pursue a doctorate in endocrinology at UC Berkeley. Her father, Donald Harris, is a Stanford University emeritus professor of economics, who emigrated from British Jamaica in 1961 for graduate study in economics at UC Berkeley.
Born in Oakland, California, Harris is a graduate of Howard University and University of California, Hastings College of the Law. Harris began her career in the Alameda County District Attorney's Office before being recruited to the San Francisco District Attorney's Office and later the City Attorney of San Francisco's office.
Endy Edeson
ELECTIONS
History professor who has accurately predicted every election since 1984 says Trump will lose
Prince Ajibade Temilade
Vincentĕ Nyam
Whether Black want make them come Africa come carry everybody but D. Trump will win after all how many black dey?