The recording comes amid public outrage over deaths of unarmed black men at the hands of police officers.
The video shows patrolman Michael Slager, from the city of North Charleston, firing eight shots at the back of Walter Scott as he runs away. The 50-year-old man falls after the eighth shot, fired after a brief pause.
North Charleston mayor Keith Summey announced the charge at a news conference in which he said Slager had made “a bad decision”.
Authorities said Mr Scott was shot after the officer had already hit the man with a stun gun after he pulled him over on Saturday because of a faulty brake light.
“When you’re wrong, you’re wrong,” Mr Summey said. “When you make a bad decision, don’t care if you’re behind the shield or a citizen on the street, you have to live with that decision.”
Slager, who has been with North Charleston police for five years, was denied bail. He was not accompanied by a lawyer. If convicted, he could face 30 years to life in prison.
The shooting comes amid ongoing public issues of trust between law enforcement and minority communities after deaths such as those of Michael Brown in Ferguson, Missouri, and Eric Garner on Staten Island, New York.
A grand jury declined to indict Ferguson officer Darren Wilson over the fatal shooting of Mr Brown last August, leading to nationwide protests. A local Black Lives Matter group, formed after Mr Brown’s death, planned a demonstration at North Charleston City Hall.
Mr Scott’s family and their lawyer, Chris Stewart, called for calm and peaceful protests. They said the murder charge showed that the justice system is working in this case.
Mr Stewart said the video forced authorities to act quickly and decisively. He added; “What if there was no video? What if there was no witness, or hero as I call him, to come forward?”
Slager’s then-lawyer David Aylor said on Monday that the officer felt threatened and Mr Scott was trying to grab Slager’s stun gun.
Mr Aylor dropped Slager as a client after the video surfaced.
The video prompted condemnations from Republican leaders in South Carolina.
Governor Nikki Haley issued a statement saying Slager’s actions were not acceptable and did not reflect the state’s values or “the way most of our law enforcement officials act”.
Republican US Senator Tim Scott, the only black US senator from a Southern state, called the shooting unnecessary and avoidable. “My heart aches for the family and our North Charleston community. I will be watching this case closely,” he wrote on Twitter.
Mr Scott may have tried to run from the officer because he owed child support, which can lead to imprisonment in South Carolina until it is paid, Stewart said.
Mr Scott had four children, was engaged and had no violent offences on his record, the lawyer said.
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