Three other police officers also face charges.
"George Floyd's horrific death, witnessed by millions of people around the world, unleashed a deep longing and undeniable demand for justice and change," said Ben Crump, a Floyd family lawyer.
"That the largest pre-trial settlement in a wrongful death case ever would be for the life of a Black man sends a powerful message that Black lives do matter and police brutality against people of colour must end," Mr Crump said.
The settlement results from a federal lawsuit the Floyd family filed in July against the city of Minneapolis.
It includes a $500,000 contribution from Floyd’s family to the community at the Minneapolis intersection where Floyd died, which has been barricaded against police access by residents and is filled with flowers and other tributes to Floyd.
Floyd's brother Rodney said the agreement is "a necessary step for all of us to begin to get some closure."
"George's legacy for those who loved him will always be his spirit of optimism that things can get better, and we hope this agreement does just that," he said.
The trial of Chauvin began earlier this week in Hennepin County’s district court on charges of murder and manslaughter.
Chauvin was helping arrest Floyd on the evening of 25 May on suspicion of his using a counterfeit $20 bill to buy cigarettes at the Cup Foods grocery store at the intersection.
Chauvin has pleaded not guilty and said he properly followed his police training.
Judge Peter Cahill has set aside about three weeks for jury selection in the high-profile case. So far, six jurors have been seated.
Hundreds rally ahead of trial for police officer accused of killing George Floyd
Last year, Floyd’s relatives sued the city, Chauvin and three other police officers involved in federal court, saying police used excessive force against Floyd in violation of his constitutional rights.
The other three officers are due to go on trial later this year on charges of aiding and abetting Chauvin in Floyd’s death, which was ruled a homicide by the medical examiner. The Minneapolis Police Department fired all four officers the day after the deadly arrest.