The recording of the conversation was posted on his Twitter account by Floyd's family lawyer Ben Crump.
"Nothing can completely correct all this, but this is at least some kind of justice," TASS quotes Biden as saying about the verdict.
According to the American leader, "this is the first step in the fight against systemic racism" in the country.
Harris, in turn, commented on the "courage and dedication" of the Floyd family.
Earlier, the court found a former police officer from Minneapolis Derek Chauvin guilty of the murder of African American George Floyd.
Chauvin's final verdict will be handed down in about eight weeks.
African American George Floyd died in late May shortly after being detained by police in Minneapolis.
One of the police officers held him down with a knee on his neck.
After Floyd's death, massive protests against racial discrimination and police violence began in the United States.