Mr Conway and Ms Ford will assume the duties of former president and CEO Lloyd Hillard, who was recently named president and CEO of the company.
Mr Conway, who was also elected as a director of the bank, has been with First Citizens since 1997 and has served as executive vice president and chief lending officer since 2004.
Ms Ford has been with the bank since 1982 and has served as executive vice president and chief operating officer since 2004.
