Biden's abrupt exit amid concerns about his mental acuity jolted the presidential race in July and Democrats scrambled to replace him with Vice President Kamala Harris as their candidate.
He will speak at 11am (3am AEDT on Friday), the White House said.
Trump's campaign said Biden had invited him to meet at the White House at an unspecified time.
In the weeks ahead, Trump will select personnel to serve under his leadership.
Harris sought on Wednesday to console the voters who had hoped she would become the first woman to win the White House.
She, like Biden, has promised to aid Trump's transition between now and his inauguration on January 20 but said she was not prepared to embrace his vision for the country.
This morning at 11 AM ET, I'll address the nation to discuss the election results and the transition.— President Biden (@POTUS) Tune in here.November 7, 2024
Former president Trump's victory, surprisingly decisive after opinion polls that had showed a neck-and-neck contest ahead of Tuesday's election, underscored how disenchanted voters had become with the economy - in particular the effect of inflation on their standard of living - border security and the direction of the country and its culture.
Hispanics, traditionally Democratic voters, and lower-income households hit hardest by inflation helped fuel the victory.
Trump prevailed in five of the seven battleground states to push him past the 270 Electoral College votes needed to win the presidency and was leading in the remaining two, Arizona and Nevada, where votes were still being tallied.
He was also on track to become the first Republican presidential candidate to win the popular vote since George W Bush two decades ago.
Republicans wrested control of the US Senate from Democrats, ensuring Trump will control at least one chamber of Congress next year.
It is not clear if they will retain their majority in the US House of Representatives, with dozens of races not yet called.
In the days and weeks ahead, Trump will select personnel to serve under his leadership, his campaign said on Wednesday.
Tesla CEO Elon Musk, the world's richest man and a prominent Trump donor, has been promised a role in his administration, as has former presidential candidate Robert F Kennedy Jr.
Ukrainian President Volodymyr Zelenskiy was among world leaders congratulating Trump.
But Trump has been critical of Biden's assistance for Ukraine in its war with Russia.
He has said he could end the war in 24 hours but has not offered a detailed plan.
The White House plans to rush billions of dollars in security assistance to Ukraine before Biden leaves office in January, sources said on Wednesday, hoping to shore up the government in Kyiv before Trump takes over.
