"Oh, absolutely. I said yes right on the spot," Fauci told NBC's "Today" in an interview.
The confirmation came a day after Biden disclosed he has asked Fauci to be his chief medical adviser and part of his administration's COVID-19 response team.
"I asked him to stay on the exact same role he has had for the past several presidents," Biden said in an interview with CNN on Thursday.
Fauci, who has served as the director of the U.S. National Institute of Allergy and Infectious Diseases since 1984, is also one of the most prominent members of the Donald Trump administration's coronavirus task force.
Ron Klain, Biden's incoming White House chief of staff and the White House Ebola response coordinator during the Barack Obama administration, tweeted on Friday that "it will be a great honor" to work with Fauci again.
Biden has made clear that it will be a top priority for his administration to address the pandemic, which has infected more than 14.2 million people in the United States, with nearly 278,000 deaths.
The Democrat also said on Thursday that he will urge Americans to wear masks for his first 100 days after taking office.
Fauci said on Friday that he has spoken with Biden about the plan, and said it was a good idea.
"He's saying 'hey folks, trust me, everybody for 100 days,'" the expert said. "Now, it might be that after that, we still are gonna need it, but he just wants it -- everybody for a commitment for 100 days."