Once a rival for the top job, the California senator of Indian-Jamaican heritage had long been considered the front-runner for the number two slot.
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-presidential candidates - Sarah Palin by the Republican party in 2008 and Geraldine Ferraro by the Democrats in 1984. Neither made it to the White House.
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.