Darren Wilson, 28, had been on administrative leave since the shooting on August 9.
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The resignation is effective immediately, said one of his lawyers, Neil Bruntrager.
Mr Wilson told the St Louis Post-Dispatch newspaper he was stepping down out of his “own free will” after the police department told him it had received threats of violence if he remained an employee.
“I’m not willing to let someone else get hurt because of me,” he told the newspaper.
The shooting led to a national debate about race and police power.
Mr Wilson fatally shot Mr Brown after a scuffle in the middle of a street, where the teenager’s body lay for several hours as police investigated and a crowd of angry onlookers gathered.
Several days of tense and at times violent protests followed, prompting Missouri Governor Jay Nixon to call in the National Guard to help.
Some witnesses have said Mr Brown had his hands up when Mr Wilson shot him.
The officer told a grand jury that reviewed the case that he feared for his life when Mr Brown hit him and reached for his gun.
The grand jury spent more than three months reviewing evidence before declining to issue any charges against Mr Wilson.
The US Justice Department is still conducting a civil rights investigation into the shooting and a separate probe of police department practices.
Several protesters in Ferguson shrugged their shoulders or expressed disinterest in the news of the resignation.
“We were not after Wilson’s job,” the Rev Al Sharpton, a civil rights activist, said. “We were after Michael Brown’s justice.”
After the shooting, Mr Wilson spent months in hiding and made no public statements.
He broke his silence after the grand jury decision, telling ABC News that he could not have done anything differently in the encounter with Mr Brown.
Mr Wilson said he has a clean conscience because “I know I did my job right”. Mr Brown’s shooting was the first time he fired his gun on the job, he said.
Asked whether the encounter would have unfolded the same way if Mr Brown had been white, the officer said yes.
Mr Wilson had no previous complaints against him and a good career record, according to Police Chief Thomas Jackson, who called him “an excellent police officer”.
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