He was joined at the special ceremony on Tuesday by vice president-elect Kamala Harris, who spoke of the collective anguish of a nation.
“For many months we have grieved by ourselves,” Harris said. “Tonight, we grieve and begin healing together.”
Mr Biden followed with his own brief remarks, telling Americans that “to heal we must remember.”
He spoke in front of 400 lights representing the pandemic victims illuminated behind him, he faced the statue of Civil War president Abraham Lincoln.
The US coronavirus death toll passed 400,000 in the final hours of Donald Trump’s presidency on Tuesday.
The number of people who have died from Covid-19 is nearly equal to the number of Americans killed in the Second World War.
Mr Biden planned to take a train into Washington before Wednesday’s Inauguration, but scratched that plan in the aftermath of last week’s Capitol riot.
He instead flew into a military airbase just outside the capital on Tuesday afternoon and then motorcaded into DC.
The city has been flooded by some 25,000 National Guard troops guarding the Capitol, White House and National Mall.
“These are dark times,” Mr Biden told dozens of supporters in an emotional sendoff in Delaware before departing for Washington. “But there’s always light.”
Mr Biden plans to issue a series of executive orders on Day One — including reversing President Donald Trump’s effort to leave the Paris climate accord.
He also plans to cancel his predecessor’s travel ban on visitors from several predominantly Muslim countries.
Mr Trump will not attend Mr Biden’s inauguration, the first outgoing president to skip the ceremony since Andrew Johnson more than a century and a half ago.
The White House released a farewell video from Mr Trump just as Biden landed at Joint Base Andrews.
Mr Trump, who has repeatedly and falsely claimed widespread fraud led to his election loss, extended “best wishes” to the incoming administration.
Mr Trump spent some of his last time in the White House huddled with advisers weighing final-hour pardons and grants of clemency.