The news conference will take place at 11 a.m. in Elizabeth City.
ABC11 will stream the news conference live.
Brown was behind the wheel of his car and outside of his house when he was shot dead on April 21 while deputies served a drug-related search-and-arrest warrant.
The police shooting, described as an "execution" by Brown's family members, has drawn national attention to the small, majority Black city in the state's rural northeastern corner.
Womble previously said Brown made "contact with law enforcement officers" with his car before they shot him.
Special coverage: The Shooting of Andrew Brown Jr.
Brown's family members and family attorneys viewed nearly 20 minutes of the body camera footage last week and said it shows a different version of events.
"We were able to see Mr. Brown sitting in his vehicle -- that he was ambushed as the sheriff's office made their way to his residence," said attorney Chance Lynch, during a news conference after they watched the video. "Appearing to be surprised. At all times his hands were visible. At all times he did not appear to be a threat."
He said, in fact, that Brown went in the opposite direction of deputies.
"What we saw at all times were police officers on the pavement unloading their weapons," he said.
Brown's son Jha'rod Ferebee said he thought the shooting never should have happened.
"My father did not deserve to die at all," Ferebee said. "He did not deserve to get killed. In any way shape or form, he did not pose any threat at all. Come court, there's no way that this could be justified. There's no way possible."
Autopsy PC, the company the family hired to perform an independent autopsy, said Brown was shot four times in the right arm, and then once -- fatally -- in the back of the head.
Gov. Roy Cooper has recommended that a special prosecutor handle the case.
The Associated Press contributed.