The lawsuit was filed at U.S. District Court in Minneapolis by Ben Crump, a civil rights attorney who has represented other families in high-profile police killings of Black men, and co-counsel Antonio Romanucci.
Crump, speaking to reporters outside the courthouse, described it as a "wrongful death, civil rights lawsuit."
Floyd's death triggered nationwide street protests against police brutality and renewed the American debate about racism in the middle of the coronavirus pandemic - just months away from the Nov. 3 presidential election.
The suit names as defendants the city of Minneapolis and four officers who participated in his arrest on suspicion of using a counterfeit $20 at a grocery store. It seeks money for compensatory, special, and punitive damages from the officers and compensatory and special damages from the city.
Derek Chauvin, a white police officer who knelt on Floyd while he was handcuffed, was arrested four days after his death. He has pleaded not guilty to second-degree murder and manslaughter charges.
Three other officers who were at the scene, J. Alexander Kueng, Thomas Lane and Tou Thao, have been charged with aiding and abetting in the case.
Floyd, 46, pleaded for his life, telling police he could not breathe.
His death, on the heels of several other high-profile police killings of African Americans, led to protests across the United States and globally, with the Black Lives Matter group demanding a revamping of law enforcement.
The U.S. Congress failed last month to agree on legislation designed to bring about changes in policing.
BEN CRUMP: Today, we have filed a federal wrongful death civil rights lawsuit on behalf of George Floyd's family and all of his children. We are going to have an important conversation that continues based on this lawsuit that documents what we have said all along. And that is it was not just the knee of Officer Derek Chauvin on George Floyd's neck for eight minutes and 46 seconds, but it was the knee of the entire Minneapolis Police Department on the neck of George Floyd that killed him.
The City of Minneapolis has a history of policies and procedures and deliberate indifference when it comes to the treatment of arrestees, especially black men, that cries out for training and discipline. Now, this is an unprecedented case. And with this lawsuit, we seek to set a precedence to make it financially prohibitive that the police won't wrongfully kill, marginalize people, especially black people in the future.