The new president entered the White House with first lady Jill Biden on Wednesday after his inauguration, and wasted no time getting to work.
He began signing 15 executive orders from the Oval Office, the first related to the coronavirus pandemic. He said there was "no time to start like today."
Biden signed an order for the US to rejoin the Paris climate accord, undoing the move made by Trump to leave the agreement.
The steps Biden is taking will also end a travel ban Trump put in place on some majority-Muslim countries.
In his inauguration speech, Biden offered a message of unity and restoration to a deeply divided country reeling from a battered economy and the raging pandemic, which has killed more than 400,000 Americans.
"To overcome these challenges, to restore the soul and secure the future of America, requires so much more than words," he said.
"It requires the most elusive of all things in a democracy: unity.
"We must end this uncivil war that pits red against blue, rural versus urban, conservative versus liberal. We can do this. If we open our souls instead of hardening our hearts."
The themes of Biden's 21-minute speech mirrored those at the centre of his presidential campaign, when he portrayed himself as an empathetic alternative to the divisive Trump, a Republican.
The inauguration itself served as a stark reminder of both the tumult that defined the Trump era as well as the pandemic that still threatens the country.
Amid warnings of possible renewed violence, thousands of armed National Guard troops circled the Capitol in an unprecedented show of force.
The National Mall, typically packed with throngs of supporters, was instead filled with nearly 200,000 US flags.
Those attending, including former Presidents Barack Obama, George W. Bush and Bill Clinton, wore masks and sat several feet apart.
Biden's running mate, Kamala Harris, the daughter of immigrants from Jamaica and India, became the first black person, first woman and first Asian American to serve as vice president after she was sworn in by US Supreme Court Justice Sonia Sotomayor, the court's first Latina member.
The president spoke forcefully about the Capitol siege when Trump backers breached the building. But Biden never mentioned his predecessor by name.
The violence prompted the Democratic-controlled US House of Representatives to impeach Trump last week for an unprecedented second time, accusing him of incitement after he exhorted his backers to march on the building to press false claims of election fraud.
"Here we stand, just days after a riotous mob thought they could use violence to silence the will of the people, to stop the work on our democracy, to drive us from this sacred ground," Biden said.
"It will never happen. Not today, not tomorrow, not ever."
Trump flouted one last convention on his way out of the White House when he refused to meet with Biden or attend his successor's inauguration, breaking with a political tradition seen as affirming the peaceful transfer of power.
Trump, who never conceded the November 3 election, did not mention Biden by name in his final remarks as president on Wednesday morning, when he touted his administration's record and hinted at a possible comeback.
He then boarded Air Force One for the last time and flew to his Mar-a-Lago retreat in Florida.
After a bitter campaign marked by Trump's baseless allegations of election fraud, Biden struck a conciliatory tone rarely heard from Trump, asking Americans who did not vote for him to give him a chance.
"I pledge this to you: I will be a president for all Americans," he said.
And I promise you I will fight as hard for those who did not support me as for those who did.
Biden also delivered a message to the rest of the world. He promised to repair alliances frayed by Trump and act as a strong partner for peace, progress and security.
World leaders issued congratulatory statements, with several US allies expressing relief at Biden's inauguration after Trump's unpredictable tenure.