“Democracy has prevailed,” he said after taking the oath of office from Chief Justice, John Roberts.
Former President Donald Trump, who has not formally conceded to Mr Biden, did not attend the ceremony.
The new president has announced a raft of executive orders aimed at reversing Mr Trump’s key policies.
Vice-President-elect Harris was sworn in ahead of Mr Biden – becoming the first woman and the first black and Asian-American person elevated to serve in a role a heartbeat from the presidency.
The inauguration took place at the US Capitol amid extra-tight security after the building was stormed by violent pro-Trump protesters in a deadly riot on 6 January.
Some 25,000 National Guards are protecting the inauguration ceremony, which is missing the traditional hundreds of thousands of spectators because of the coronavirus pandemic.
Mr Trump left the White House for the last time as president shortly after 08:00 (13:00 GMT). He boarded a helicopter, flew to the nearby Andrews Air Force base, and has now arrived in Florida.
He is the first president not to attend his successor’s inauguration since 1869.
In his inaugural address, Mr Biden said it was a day of “history and hope”. “My whole soul is in putting America back together again,” he added.
Highlighting a message of unity after the turbulent years of the Trump presidency, he promised to be a leader “for all Americans” – including those who voted against him.
Among those attending the ceremony are three of his predecessors: Barack Obama – under whom Mr Biden served for eight years as vice-president – Bill Clinton and George W Bush.
The 78-year-old first walked into the Capitol as a senator from Delaware in 1972.
Biden unsuccessfully ran for president twice – in 1987 and 2008 – before becoming Obama’s vice-president.
Even during this latest campaign, there were moments early on when it seemed he might not become the Democratic nominee.
Biden wrapped up his inaugural address warning that America must not “turn inward” – both as individuals retreating into their “competing factions” and as a nation on the world stage.
“We will repair our alliances and engage with the world once again,” he said.
Biden pledged to give the effort to rebuild and repair the US his full attention.
He noted, rightfully, that he – and the rest of America – “will be judged by how we resolve these cascading crises of our era”.