Joe Biden was sworn in as the 46th US president and Kamala Harris was sworn in as 49th vice-president, the first woman and the first black and Asian-American person to serve.
The new president has announced a raft of executive orders aimed at reversing Mr Trump’s key policies.
The inauguration took place at the US Capitol. There is 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 ceremony, which is missing the traditional hundreds of thousands of spectators because of the coronavirus pandemic.
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 Trump years, he promised to be a president “for all Americans” – including those who voted against him.
Donald Trump, who has not formally conceded to Mr Biden, did not attend the ceremony. Mr Trump was the first president not to attend his successor’s inauguration since 1869. He left the White House at about 08:00 on Wednesday, and flew to the nearby Andrews Air Force base for Florida.
Attending the ceremony were three of his predecessors: Barack Obama – under whom Mr Biden served for eight years as vice-president – Bill Clinton and George W Bush.
Former Vice-President Mike Pence also attended. He skipped Mr Trump’s farewell military salute event.
The inauguration ceremony included musical performances by Lady Gaga – who sang the national anthem – as well as Jennifer Lopez and Garth Brooks.