Democracy has prevailed," he said after taking the oath of office from Chief Justice John Roberts.
Donald Trump - who has not formally conceded the presidency to Mr Biden - snubbed the inauguration ceremony, in a departure from longstanding precedent.
The new president has announced a raft of measures reversing Trump policies.
Kamala Harris was sworn in as vice-president ahead of Mr Biden.
She is the first woman - and the first black and Asian-American person - to serve in a role, a heartbeat from the presidency.