"When you're wrong, you're wrong," North Charleston Mayor Keith Summey said, announcing the arrest. "When you make a bad decision, I don't care if you're behind the shield or a citizen on the street, you have to live with that decision."
The incident on Saturday began after Scott's car was stopped for having a broken rear light, local media reported.
Anthony Scott said that because of the video, "we have received the truth" and "through the process, justice has been served".
Chris Stewart, a lawyer for Scott's family, called the passer-by who recorded the video a "hero".
The shooting occurred as heightened scrutiny is being placed on police officer shootings, particularly those that involve white officers and unarmed black suspects.
A grand jury declined to indict Ferguson, Missouri officer Darren Wilson over the fatal shooting of Michael Brown last August, leading to nationwide protests.
US police: Controversial recent killings
April 2015: Walter Lamer Scott, 50, is shot eight times in South Carolina as he runs away from Officer Michael Slager. Mr Scott dies at the scene. The shooting is captured on video and Mr Slager is charged with murder.
December 2014: Jerame Reid, 36, is shot dead during a routine traffic stop in New Jersey. An officer claims Mr Reid was reaching for a gun, but video footage seems to suggest he was attempting to step out of the car, hands raised.
November 2014: Tamir Rice, a 12-year-old boy, is shot dead in a playground by Cleveland police after a local resident reports he is pointing a gun at passers by. The gun turns out to be a toy. A grand jury will decide whether police will face charges.
July 2014: Eric Garner, an asthma sufferer, is stopped by police in New York and placed in a chokehold after refusing to be handcuffed. He dies despite repeatedly telling officers he can't breathe. No police are charged.
March 2014: James Boyd, an unarmed homeless man camping in Alberquerque, is shot dead by two officers. Video of the incident leads prosecutors to say the officers acted with "deliberate intention" and they are charged.