Grant's family initially sought $50 million for the 2009 New Year's Day shooting at the Fruitvale BART station, but both parties agreed to $1.5 million after an 11-hour settlement conference.
BART's attorney says the deal should protect Grant's daughter Tatiana for the rest of her life.
"You can't replace a life, but our system of civil law, the tort system, says we must compensate if there's going to be a wrong," Dale Allen said.
Grant's mother Wanda Johnson has yet to settle her civil case.
Johannes Mehserle, the officer accused of shooting Grant, is due to go on trial for murder later this year.