Rashid Ali Bynum, 28, of Portsmouth, Virginia, was taken into custody on Tuesday morning just before 11 a.m.
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Police say Bynum knew Dwumfour from the Champions Royal Assembly Church in Newark and they worked together at the church.
Dwumfour was fatally shot inside her car on Feb. 1 after she dropped someone off in Sayreville.
Surveillance footage captured Bynum running from the scene after the shooting, Middlesex County Prosecutor Yolanda Ciccone said. She also said a mobile phone belonging to Bynum indicated travel from Virginia to New Jersey at the time of the murder.
Bynum was charged with first-degree murder, second-degree unlawful possession of a handgun, and second-degree possession of a handgun for an unlawful purpose.
"The murder has shaken the community and no arrest will bring back the late councilwoman," Ciccone said.
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Though Dwumfour was a Newark native who still has family living there, she was living in Sayreville as a single mother. She had just recently married a pastor who lives in Nigeria.
"There are no words that can be said to you to make you whole," Attorney General Matthew Platkin said, addressing her relatives in the room. "I did not know Eunice. I wish I had. But I know that she was a public servant."
Dwumfour, 30, was the first sitting elected official to be killed in New Jersey in recent memory.
Bynum is awaiting extradition to New Jersey where he will then be held at the Middlesex County Adult Correctional facility pending a pre-trial detention hearing in Superior Court.