Last week, the Los Angeles District Attorney was looking to modify the singer's probation, alleging the star failed to provide "credible, competent or verifiable evidence" that he completed his court-ordered community service.
Norwood was the one who signed off on Brown's community service hours.
In a press release on Tuesday, Richmond Mayor Dwight C. Jones stated he had accepted Norwood's resignation.
"I know that in many ways, the Richmond Police Department and our city is better off because of his involvement, his dedication, and his concern and care for our communities," the mayor's statement read, in part, regarding Norwood. "But we've reached a mutual agreement in that his time as Richmond's Police Chief has come to an end."
Brown had been ordered to complete 180 days of community labor after his brutal 2009 attack on Rihanna as part of his five-year probation sentence for assault.
However, Los Angeles Deputy District Attorney Mary Murray filed a 19-page motion on Feb. 5, claiming there are "significant discrepancies" in the reports submitted by Richmond, Va., police as proof that Brown performed six months of community labor. She said the records in question are "at best, sloppy documentation and, at worst, fraudulent reporting."
The Los Angeles District Attorney's office tells E! News it will not be making any comments or releasing any statement regarding Norwood's resignation.