Biden spoke after telephoning Floyd's family, telling them, We're all so relieved.
Before Tuesday's guilty verdicts were read out, Biden said he was praying for "the right verdict in the trial of Chauvin.
Telephoning Floyd's family later, he said of himself and Harris: We're all so relieved.
Chauvin was convicted of two counts of murder and one of manslaughter in the death of Floyd, a case that sparked a national reckoning on race and policing.
Biden said he hoped the verdict would give momentum to congressional police reform efforts.
Floyd family attorney Ben Crump posted video on Twitter of a phone call from Biden and Harris to the family.
Asked by a family member how he was doing, Biden said, Feeling better now. Nothing is going to make it all better, but at least now there is some justice.
This is a day of justice, Harris told the family after joining Biden to watch the verdict in the private dining room off the Oval Office.
Speaking hours ahead of the verdict, while the jury was deliberating in Minneapolis, Biden said he called Floyd's family on Monday to offer prayers and could "only imagine the pressure and anxiety they're feeling.
They're a good family and they're calling for peace and tranquility no matter what that verdict is, Biden said a few hours before the verdicts were announced.
I'm praying the verdict is the right verdict. I think it's overwhelming, in my view. I wouldn't say that unless the jury was sequestered now.
Biden said he was only weighing in on the trial into the death of Floyd, who died with Chauvin's knee on his neck, because the jury in the case had already been sequestered.
The president has repeatedly denounced Floyd's death but had previously stopped short of weighing in on Chauvin's trial, with White House officials saying it would be improper to speak out during active judicial proceedings.
On Tuesday, White House press secretary Jen Psaki repeatedly refused to explain Biden's comments, doing nothing to dispel the impression that he thought Chauvin should be found guilty.
Floyd's brother, Philonise Floyd, told NBC's Today show that Biden knows how it is to lose a family member ... so he was just letting us know that he was praying for us and hoping that everything would come out to be OK.
On Capitol Hill, Republicans as well as Democrats said they were relived at the verdict and predicted it could give momentum to policing reform legislation that has been proposed in both the House and Senate.
I think the verdict just reinforces that our justice system continues to become more just, said Tim Scott of South Carolina, the only Black Republican senator.
This is a monumental day in many ways, in my opinion.
The Congressional Black Caucus watched the verdict together in the Capitol, and members hugged and fist pumped after the verdict was read.
The room was filled with emotion and gratitude, said Georgia Rep. Hank Johnson. Black lives mattered to this jury. And I'm very gratified at the verdict, very happy at the swiftness of the verdict. ... It's a vindication of justice in America.
House Speaker Nancy Pelosi joined the Black Caucus shortly afterward at a news conference outside, where she said she had spoken to Floyd's family just before the verdict.
She said she called to say to them, Thank you, God bless you, for your grace and your dignity, for the model that you are appealing for justice in the most dignified way.'
Thank you George Floyd for sacrificing your life for justice, Pelosi said. Because of you, and because of thousands, millions of people around the world who came out for justice, your name will always be synonymous with justice.
The verdict and the aftermath will be a test for Biden, who has pledged to help combat racism in policing, helping African Americans who supported him in large numbers last year in the wake of protests that swept the nation after Floyd's death and restarted a national conversation about race.
But he also has long projected himself as an ally of police, who are struggling with criticism about long-used tactics and training methods and difficulties in recruitment.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)
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