President Joe Biden spoke to former President Donald Trump on the phone Wednesday to congratulate him on winning the presidency, the White House said in a statement.

"President Biden expressed his commitment to ensuring a smooth transition and emphasized the importance of working to bring the country together," the White House said.

Biden invited Trump to meet with him at the White House, the statement said.

Trump campaign spokesperson Steven Cheung said the meeting "will take place shortly."

"President Joe Biden called President Donald J. Trump to congratulate him on his victory and extended an invitation to the White House to ensure a smooth transition between the current Administration and the incoming Administration. President Trump looks forward to the meeting, which will take place shortly, and very much appreciated the call," Cheung said in a statement.

Biden also spoke to Vice President Kamala Harris on the phone Wednesday to congratulate her on "her historic campaign," the White House said.

Later, following Harris' concession speech to the nation on Wednesday afternoon, Biden released a statement praising Harris, saying she has been a "tremendous partner and public servant full of integrity, courage and character."

"Under extraordinary circumstances, she stepped up and led a historic campaign that embodied what's possible when guided by a strong moral compass and a clear vision for a nation that is more free, more just, and full of more opportunities for all Americans," Biden said.

Biden said choosing Harris as his running mate was "the best decision" he made.

"Her story represents the best of America's story. And as she made clear today, I have no doubt that she'll continue writing that story," Biden said.

"She will continue the fight with purpose, determination and joy. She will continue to be a champion for all Americans. Above all, she will continue to be a leader our children will look up to for generations to come as she puts her stamp on America's future," Biden added.

Trump and Harris also spoke by phone on Wednesday, according to the Trump campaign. Harris told Trump she will work with Biden to ensure a peaceful transfer of power, unlike the transition in 2020, according to an email Harris campaign chair Jen O'Malley Dillon sent to campaign staff.

Biden plans to talk about the election results and the transition on Thursday, according to the White House.

Harris' defeat came as Trump clinched wins in the swing states of Pennsylvania, Georgia and Wisconsin overnight. Trump went on to win another swing state, Michigan, on Wednesday.

ABC News' Katherine Faulders contributed to this report.