Overcash has spent his entire law enforcement career with the Concord Police Department since becoming a patrol officer in 1983, officials said in a statement.
In 2003, after working in various roles in the department, he was promoted to major and supervised the department's first Special Investigations Unit, which was called on to investigate serious crimes, as well as unsolved homicides.
As deputy chief, Overcash will replace Guy Smith, who was promoted to police chief last year.
In his new role, Overcash will help with the overall operation of the department, and he'll also be involved in the development of the budget, policies and coordination with other agencies, officials said.
"I am extremely grateful for the opportunity I've been given in this great community and department," Overcash said in a statement.
Overcash graduated from Concord High School and then received his undergraduate and Master of Business Administration degrees from Pfeiffer University. He's a member of the Concord Rotary Club and Forest Hil United Methodist Church, where he works with youth.
"Deputy Chief Overcash will be an excellent addition to the Police Department's top management," said Assistant City Manager and former police chief Merl Hamilton. "He has a lengthy and varied career in law enforcement. The fact his career has been spent entirely in Concord, as has that of Chief Smith, makes the Police Department's commitment to this community even stronger."
Overcash will officially begin his new role on Sept. 3.
Concord Police Deputy Chief Allen Overcash