The head of state was captured by journalists as he boarded a plane that was to take him from his home state of Delaware to Washington.
"I'm feeling well," Biden told reporters as he boarded Air Force One at Dover airport.
As noted by the pool correspondent, Biden did not answer questions about his reasons for withdrawing from the presidential race and whether he is confident in the victory of the current Vice President Kamala Harris, who is likely to become the Democratic candidate.
Biden was en route to the White House, where he is expected to arrive later this afternoon.
It is expected that the president will address the nation the next day, where he will touch on the topic of his withdrawal from the race and outline the prospects for the final months of his term.