Biden said the US faced a "very dark winter" and the "worst wave yet", and Americans had to put aside political differences to tackle Covid-19.
He has named a new task force and vowed to "follow the science" as he puts together his transition team.
Donald Trump still refuses to concede defeat and is challenging key results. He is taking legal action in several states.
Biden's victory was declared on Saturday but it remains a projection, with a number of states still counting ballot papers. He leads Trump in the nationwide vote by about 4.5 million.