Neil Bruntrager told media the resignation was effective immediately.
Darren Wilson himself has been quoted by as saying he had taken the step because of threats of violence if he stayed.
Ferguson and other US towns and cities saw rioting after a jury decided Darren Wilson, 28, should not be charged.
The August 9 shooting in the St Louis suburb and last week’s state grand jury decision triggered a nationwide debate over relations between black communities and law enforcement.
The St Louis Post-Dispatch newspaper said Darren Wilson had decided to step down after his police department received threats that violence would follow if he stayed on as an employee.
The newspaper published what it said was his resignation letter, which read: “I have been told that my continued employment may put the residents and police officers of the City of Ferguson at risk, which is a circumstance that I cannot allow.
“For obvious reasons, I wanted to wait until the grand jury made their decision before I officially made my decision to resign.
“It was my hope to continue in police work, but the safety of other police officers and the community are of paramount importance to me. It is my hope that my resignation will allow the community to heal.”
In a subsequent telephone interview on Saturday evening, the paper quoted Darren Wilson as saying: “I’m resigning of my own free will. I’m not willing to let someone else get hurt because of me.”
He added that resigning was “the hardest thing I’ve ever had to do”.
Earlier this week, Darren Wilson told media that before the shooting, Michael Brown had pushed him back into his car, hit him and grabbed at his drawn gun, and said that he felt “like a five-year-old holding on to Hulk Hogan”.
The policeman said he had feared for his life.
Michael Brown’s supporters said he was attempting to surrender to the policeman when he was shot. Some witnesses said the teenager, who was unarmed, had his hands up.
However, the state prosecutor said physical evidence had contradicted some of the witness statements.
Michael Brown was killed after being shot six or seven times.
Many in the African-American community had called for Darren Wilson to be charged with murder, but after three months of deliberation a Missouri grand jury – of nine white and three black members – made no recommendation of charges.
The decision means Darren Wilson will not face state criminal charges over the shooting.
The US justice department has also launched a federal investigation into whether Darren Wilson violated Michael Brown’s civil rights.
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