The president said he was acting on racial injustice and discrimination because “not only it is the right thing to do but we will all be better off for it”.
Mr Biden signed executive orders stopping the Department of Justice from renewing contracts with private prisons, and others aimed at ending discriminatory housing practices, respecting sovereignty of tribal governments, and fighting xenophobia against Asian Americans and Pacific Islanders in the wake of Covid-19.
“In my campaign for president I made it very clear that the moment had arrives as a nation where we faced deep inequity in the American system that has plagued our nation for far too long," said Mr Biden.
"Those 8mins 46 secs that took George Floyd’s life opened the eyes of millions of Americans and millions of people all around the world.
“It was the knee on the neck of justice and it stirred the consciousness of tens of millions of Americans and it would not be forgotten. In my view it marked a turning point in this country’s attitude towards racial justice.”
Mr Floyd, 46, died last May when he was arrested by police outside a shop in Minneapolis, Minnesota.
Footage of the arrest shows a white police officer, Derek Chauvin, kneeling on Mr Floyd's neck while he was pinned to the floor.
And the transcript of police bodycam footage showed Mr Floyd told officers he could not breathe more than 20 times as he was being detained.
Chauvin faces charges of second-degree unintentional murder and a second-degree manslaughter charge in Mr Floyd's, which sparked nationwide protests.
Mr Biden recalled meeting Mr Floyd’s daughter, Gianna, following his death and the impact that the youngster had on him.
“When I met with the family I leaned down and said hi, and she looked at me and said ‘daddy changed the world’ and I believe she was right,” he added.
“Not because this kind of injustice stopped, it clearly hasn’t, but because the ground has shifted, because it has changed minds and mindsets and it laid the groundwork for progress.”
Mr Biden also addressed the high rates of Covid-19 deaths among the Black and Latino communities, whom he said are dying at three times the rate of the white community.
“That is not white Americans’ fault, it is just a fact," he said.
And he praised the younger generation of Americans as the “most progressive, thoughtful and inclusive generation this country has ever seen”.
Justice Department directed to not renew private prison contracts
Administration condemns and denounces anti-Asian bias in wake of Covid-19 pandemic
Memo to Department of Housing and Urban Development to ‘redress historical racism in federal housing policies’
Reaffirmed federal government's commitment to tribal sovereignty and consultation
Mr Biden also cited the deadly Capitol riots on 6 January, in which five people died, as a sign the country needed to act.
“It is just weeks since all America witnessed a group of thugs, insurrectionists, political extremists and white supremacists violently attack the capital of our democracy so now is the time to act, it is time to act because that is what faith and morality calls us to do,” he said.
And he called on Americans to “lift each other up” rather than hold each other back.
“For too long we have allowed a narrow, cramped view of the promise of this nation to fester,” added Mr Biden.
"We have bought the view that America is a zero sum game. If you succeed, I fail. If you get ahead, I fall behind. If you get the job, I lose mine. And maybe worst of all, if I hold you down, I lift myself up.
“When we lift each other up we are all lifted up, and when anyone of us is held down we are all held back.”
Mr Biden also announced that his administration had ended Donald Trump’s “harmful” ban on sensitivity training and had axed Mr Trump’s “offensive and counterfactual” 1776 Commission.
“Unity and healing must begin with understanding and truth, not ignorance and lies," said Mr Biden.
The president also addressed the government’s ban on renewing deals with private prisons.
“This is the first step to stop private corporations from profiting off incarceration that is less humane and less safe, as studies show,” he added.
The president also called for lawmakers to “restore and expand” the Voting Rights Act, named after the late congressman John Lewis.
“I ran for president as I believe we are in a battle for the soul of this nation, and the simple truth is our soul will be troubled as long as systemic racism is allowed to persist,” said Mr Biden.
“We are not going to eliminate it over night but it is corrosive, destructive and costly.
"We are less prosperous, less successful, less secure, we must change and I know it is going to take time, but I know we can do it and I firmly believe the nation is ready to change.”
He added that the White House and the federal government would be “part of that effort” to eliminate systemic racism.