In the primary, the candidates knocked out their three competitors, with Arrington earning 5,713 votes, or 46 percent, and Muhammad garnering 3,889 votes, or 31 percent.
The winner will be unopposed on Election Day, Nov. 4.
Arrington, 42, is an attorney.
He graduated from the University of Virginia in Charlottesville, Va., in 1993 with a bachelor’s degree in economics and earned his law degree in 1996 from Emory University.
Arrington is married with four children.
His previous political experience is a 2012 run for District 62 in the state House of Representatives.
Arrington’s top three issues are reducing crime, fixing county infrastructure and buildings, and increasing arts and recreation opportunities for seniors and youth.
He said he is the best person for the job because of his experience as a husband, father, attorney and community servant.
“I want to leverage my experience for the benefit of the citizens of Fulton County,” he said. “I am not afraid to stand up for what is right and to speak out against things that are wrong.”
Muhammad, 63, is the executive director of the nonprofit Atlanta Victim Assistance.
She earned bachelor and master degrees from Southern New Hampshire University in 2003 in community economic development with a focus on economic development.
Muhammad is widowed, the mother of three children and grandmother of 10.
Her political experience is 16 years on the Atlanta school board.
Muhammad said her top three issues are fiscal responsibility, health and human services, and economic development.
She said she is the best person for the job because she is a proven leader who will help taxpayers get quality county services.
“I choose to serve because it allows me to stand up for people who are disenfranchised, who are victimized, who are silenced,” Muhammad said. “I’ve got a big voice and I use it to speak out for the underdogs of society.”