The council had met several times in the past few months to receive advice from city attorney Brady Hair on a potential lawsuit by Scott's family.
Scott, an unarmed 50-year-old black man, was filmed being shot to death while running from North Charleston police officer Michael Slager, who was fired from his job and charged with murder.
A bystander recorded the April 4 shooting with a cellphone.
"It could have been a trillion dollars. It would never bring my son back. But I thank them for what they did," Scott's mother, Judy, said of the settlement.
Chris Stewart, an attorney for Scott's family, said the payout was the largest pre-lawsuit settlement in the history of South Carolina and one of the largest in the United States.
New York City agreed to pay $5.9 million to the family of Eric Garner, over his killing in chokehold by an NYPD officer, which was captured on bystander video, Baltimore reached at $6.4 million settlement with the family of Freddie Gray, whose death in a police van prompted murder charges for six officers.
Steward said the Scott family's settlement with North Charleston would take care of Scott's four children for the rest of their lives.
"It was a bittersweet victory," Scott's brother Anthony said. "The family still wants justice for my brother and this was a step in the right direction."
Anthony Scott said the family plans to donate some of the money from the settlement to disaster relief for victims of the recent floods in South Carolina.
Mayor Keith Summey said he was pleased with the settlement.
"The family took steps to keep the community calm, and for that the city is thankful," he said. "This is a very difficult period for the Scott family. I know they are glad to have this part behind them so their healing process can continue."
In the immediate aftermath of the shooting, Scott's family called for peace. Some, have credited the family's action — along with the officer's speedy arrest — with staving off the protests and violence that have erupted in other cities where unarmed black men have died during encounters with police.
Before the video was brought to the attention of authorities, Slager had told investigators that Scott tried to grab his gun and Taser. But prosecutor Scarlett Wilson said Scott was running away and the only time Slager could be seen running was to go back, pick up the Taser and then drop it by Scott's body.
Slager was fired following his arrest on the murder charges and has been detained in solitary confinement.
Slager was indicted on a murder charge in June and a judge refused to set bond last month, saying his release would "constitute an unreasonable danger to the community."
Slager faces from 30 years to life in prison without parole if he is convicted of murder. There were no aggravating circumstances such as robbery or kidnapping, so the death penalty doesn't apply in the case, the prosecutor has said.
Al Jazeera with wire services